Device for processing non-orthogonal coordinate system error in high-dimensional motion system

Abstract

The embodiment of the invention provides a device for processing non-orthogonal coordinate system errors in a high-dimensional motion system, which can perform modeling on the high-dimensional motion system by using a straight coordinate system and a trigonometric function coordinate system respectively and perform cross validation by using the two models so as to reduce errors generated during projection from a high-dimensional space to a low-dimensional space. The embodiment of the invention aims to provide a modeling method which is simpler and more visual and based on traditional physics for the specific embodiment of calculation of the rotation period of the earth in a patent application of a method and a device for predicting the motion state of an object with the patent application number of 202410836284.1.

Description

Technical Field

[0001] The present invention relates to the application field of computer mathematics in physical modeling, and in particular to a method and device for processing non-orthogonal coordinate system errors in a high-dimensional motion system. Background Art

[0002] In the specific embodiment part of the patent application "A method and device for predicting the motion state of an object" (patent application number 202410836284.1, hereinafter referred to as "Reference 1"), a method for calculating the earth's rotation period is disclosed. This calculation method is modeled and derived based on the conclusions of special relativity and quantum mechanics, and special relativity and quantum mechanics are characterized by theoreticalization and abstraction.

[0003] The calculation of the Earth's rotation period itself is an interesting topic. The present invention hopes to remodel and derive the calculation method of the Earth's rotation period in Reference 1 based on traditional physics. Compared with Reference 1, the method described in the present invention has the advantages of being intuitive, easy to understand and easy to implement.

[0004] Let us first repeat the calculation process of the Earth's rotation period in Reference 1 as follows.

[0005] Assumptions:

[0006] 1.E 1 The energy for the earth's rotation;

[0007] 2, ν 1 is the Earth's rotation frequency;

[0008] 3.E 2 It is the energy interference term of the Moon at perihelion and aphelion when it orbits the Earth with the Sun as the reference frame. In this example, it is exactly the energy difference between the Moon at perihelion and aphelion.

[0009] Let the speed of the Earth's revolution around the Sun be v 1 , the speed of the moon's revolution around the earth is v 2 , then the energy difference between the moon at perihelion and aphelion is:

[0010] E 2 =E 远日 -E 近日 =(v 1 +v 2 )^2-(v 1 -v 2 )^2=4v 1 v 2

[0011] (Formula 1)

[0012] 4, ν2 is the frequency of change of the speed of the moon's linear motion, that is, the reciprocal of the time interval between the moon's perihelion and aphelion.

[0013] Then we have:

[0014] E 1 * 1 =(E 月_远日 -E 月_近日 )*ν 2

[0015] (Formula 2)

[0016] By calculating based on formula 2, we can get the Earth's rotation period.

[0017] There are three operation symbols in Formula 2, representing three different physical operations, which require three modules based on traditional physics modeling:

[0018] (1), Flat coordinate system modeling module.

[0019] It corresponds to the minus sign in formula 2, which is actually v in formula 1. 1 *v 2 The multiplication sign in the subterm. 2 is the energy interference term (i.e., contains v 1 v 2 ), which is exactly the energy difference between the moon at perihelion and aphelion. What needs to be modeled is why the energy interference term is used as a separate dimension instead of other calculation methods, such as not taking the average kinetic energy of the moon as a separate dimension. This will involve the velocity cross product term modeling module.

[0020] The main function of this module is to complete the modeling of energy interference terms in traditional physics.

[0021] (2), trigonometric function coordinate system modeling module.

[0022] This corresponds to the multiplication sign in equation 2. This will involve the orthogonalization processing module between dimensions. In particular, compared with the de Broglie relation, equation 2 mainly adds a product sub-term on the left side of the equation (i.e., multiplying by ν 1 sub-item), the corresponding physical meaning is to add frequency to the original straight motion energy, which represents the orthogonalization between dimensions.

[0023] The main function of this module is to complete the modeling of the relationship between energy and frequency in traditional physics.

[0024] (3), Cross-validation module.

[0025] This corresponds to the equal sign in equation 2. Equation 2 is a relationship between the product of two energies and frequencies, or a relationship between two actions. What needs to be modeled is why the rotation of the Earth is balanced with the action balance in the two dimensions.

[0026] The main function of this module is to complete the modeling module of action equipartition in traditional physics, map the system from the flat coordinate system to the trigonometric function coordinate system, and realize the cross-measurement of the system in the two coordinate systems. Summary of the invention

[0027] An embodiment of the present invention provides a device for processing non-orthogonal coordinate system errors in a high-dimensional motion system, which can model the high-dimensional motion system using a straight coordinate system and a trigonometric function coordinate system respectively, and use the two models for cross-validation to reduce the errors generated when projecting from a high-dimensional space to a low-dimensional space.

[0028] On the other hand, the embodiment of the present invention can perform orthogonal processing on a system that mixes straight coordinates and trigonometric function coordinates, thereby removing errors or uncertainties caused by non-orthogonalization of coordinates.

[0029] The embodiment of the present invention includes: a straight coordinate system modeling module, a trigonometric function coordinate system modeling module, a cross-validation module and other modules.

[0030] 101. Flat Coordinate System Modeling Module

[0031] Modeling based on a straight coordinate system is to model the system based on methods such as velocity and acceleration. This module is used to process (v 1 +v 2 )^2=v 1 ^2+2v 1 v 2 +v 2 ^2. Except for v 1 v 2 Item (v 1 v 2 Item refers to the inclusion of v 1 v 2 Except for the sub-items, the other items are basically simple and intuitive, and do not require special skills. I will not repeat them below. Almost all the work in this module is focused on v 1 v 2 Understanding and handling of items.

[0032] 1011. Velocity cross product orthogonal analysis submodule

[0033] In the straight coordinate system, v 1 v 2This is why we need to introduce trigonometric coordinates to analyze the system again. Intuitively, when a straight coordinate system is used to model a high-dimensional space in a low-dimensional space, the coordinate system is straight but non-orthogonal, and v 1 v 2 Intuitively, the term represents the non-orthogonality between coordinate systems. The following is an explanation based on a specific physical scenario.

[0034] Similar to v 1 v 2 Such terms correspond to the "mixing" of two quantities, or "rotation" in vector and matrix calculations. 1 v 2 When it appears in the expression of energy, it is the "interference term energy" in reference 1. In addition to the expression of energy, such terms may also appear in the expressions of magnetism, path length of moving objects, etc. Later, the various expressions of energy, magnetism, length, etc. containing v 1 v 2 The terms are collectively referred to as “velocity cross product terms”.

[0035] One of the goals of this module is to map the interference term energy to a motion in an independent dimension that is orthogonal to other dimensions in the system. Because trigonometric coordinates can easily construct high-dimensional orthogonal spaces, this dimension is mapped to a trigonometric coordinate. The explanation is as follows.

[0036] E in Formula 2 2 , calculated by the following method.

[0037] Let the speed of the Earth's revolution around the Sun be v 1 , the speed of the moon's revolution around the earth is v 2 , then the energy difference between the moon at perihelion and aphelion is (omitting the coefficient 1 / 2m):

[0038] (v 1 +v 2 )^2-(v 1 -v 2 )^2=4v 1 v 2

[0039] This is a file containing v 1 v 2 The terms of the product are relatively difficult to deal with. In physics, we generally tend to eliminate such terms by transforming the coordinate system.

[0040] As mentioned in reference 1, the interference term energy corresponds to the special relativity effect, and the special relativity effect corresponds to the magnetic field in electrodynamics. Therefore, the magnetic field is used as an example to illustrate some properties of the interference term energy. In the magnetic field, the interference term energy includes v1 v 2 The term will appear in the expression of magnetic field energy and in the expression of magnetic force. Because force is more intuitive than energy, we will take magnetic force as an example to explain the expression with v 1 v 2 How the terms of are understood and modeled.

[0041] It should be noted that it is possible to establish a model that includes the velocity v at least from the perspectives of motion path length, magnetic force, and acceleration. 1 v 2 and acceleration a. The equation for the length of the motion path is more general, and the relevant technology has been solved after the special theory of relativity introduced the principle of the constancy of the speed of light. The magnetic force is more intuitive, so the following discussion will only focus on the magnetic force. 1 v 2 and acceleration a. Although only magnetism is discussed below, the special theory of relativity shows that after the principle of the constancy of the speed of light is extended from electrodynamics to ordinary moving objects, many conclusions in electrodynamics can be extended to ordinary dynamics. The point I want to make here is that a system containing multiple speeds is multidimensional, and the cross-product terms of speed in expressions such as energy, magnetism, and length can be understood as additional effects produced in the process of projecting from high dimensions to low dimensions; conversely, for systems containing v 1 v 2 It is a better method to perform high-dimensional modeling on the items.

[0042] Assume that two objects are observed in the current reference frame, object 1 is moving at a speed v 1 Moving, object 2 moves at a speed v 2 motion; there is another reference frame 3 with speed v 3 sports.

[0043] When an object is charged Figure 3 As shown, two moving objects interact through the electromagnetic field, where the force exerted on object 2 by the magnetic field of object 1 is:

[0044] F m =kq 1 q 2 v 1 v 2 / r^2

[0045] (Formula 3)

[0046] The focus of the problem is on various methods for v in formula 3 1 v 2 Newtonian mechanics, electromagnetism, relativity and interference term energy have different understandings of this.

[0047] First of all, we need to explain why v 1 v2 The sub-items are incomprehensible.

[0048] One of the beliefs in physics is that all inertial reference frames are equal. However, "equality" does not have a precise mathematical meaning. Here are two examples related to "equality".

[0049] (1) For Newtonian mechanics, F = ma, which does not directly include the velocity v. Therefore, the acceleration a is related to any velocity v (v 1 or v 2 or v 3 ) are not directly related.

[0050] (2) The magnitude of the force acting on an object moving in a fluid is related to the relative velocity (v 1 -v 2 ) is related. It should be noted that the magnitude of this force is related to the velocity v of the reference frame. 3 It is irrelevant, regardless of v 3 What value should the relative speed (v 1 +v 3 )-(v 2 +v 3 )) = (v 1 -v 2 ) has been put into 3 Therefore, the magnitude of the drag is only related to the relative speed and has nothing to do with the speed of the reference system.

[0051] However, in formula 2, v 1 v 2 The result of the sub-item is different from the above two examples. When transformed to reference system 3, the velocity v of reference system 3 3 Will be added to v through the vector synthesis of the velocity 1 ->(v 1 +v 3 ) and v 2 ->(v 2 +v 3 ) (the symbol -> refers to the transformation accompanying the coordinate system transformation), and (v 1 +v 3 )*(v 2 +v 3 ) In general, v will be retained 3 So v in formula 2 1 v 2 The result of the sub-term is the velocity v of the reference frame 3 are relevant.

[0052] v 1 v 2 The velocity v of the subterm and the reference frame 3is relevant, and this subterm is included in the expression for the force and the corresponding acceleration, which is where it is difficult to understand.

[0053] In electromagnetism, there is a complex mechanism to ensure that the speed (v 3 When taking various values ​​of , the resultant force of the electric and magnetic forces is "coordinated", but the "coordination" here does not mean equality, but is based on the complex transformation of Maxwell's equations. Here we only focus on the magnetic force and do not discuss the coordination mechanism between electricity and magnetism.

[0054] 1012. Reference frame translation modeling submodule

[0055] Some existing pairs 1 v 2 The method by which the child item is processed.

[0056] There are some simplifications 1 v 2 Sub-item processing method. Obviously, we choose charge 1 as the reference system (that is, let v 1 +v 3 = 0), or choose charge 2 as the reference system (that is, let v 2 +v 3 =0), so one of the two charges is stationary, and the magnetic force (v 1 +v 3 )*(v 2 +v 3 ) = 0, thus eliminating the interference term (magnetic term). This method is called coordinate translation method below. Newtonian mechanics' treatment of electromagnetism and special relativity are both related to coordinate translation method, as explained below.

[0057] (1) When analyzing electromagnetism based on Newtonian mechanics, it is customary to choose charge 1 as the reference system (that is, let v 1 +v 3 = 0), so that charge 2 is only affected by the electrostatic field, and the result is the same as v 3 Furthermore, although the force on charge 2 will retain v when other reference frames are chosen 3 term, but the result is equivalent to the result after choosing charge 1 as the reference system and processing it through the "coordination mechanism" of electricity and magnetism.

[0058] This makes people believe that v 1 v 2 The reference frame velocity v contained in the sub-item 3 In the end, the dynamic result (i.e., acceleration a) and the reference frame velocity v can be eliminated. 3 It doesn't matter, but v 3 The role of is limited to the "coordination" mechanism of electricity and magnetism.

[0059] So from this point of view, although "the acceleration of electromagnetic objects is related to the velocity of the reference frame" and "each inertial reference frame is equal" seem to be in direct contradiction, there is a complex electromagnetic "coordination" mechanism separating the two. This contradiction may be the characteristic of electromagnetism and will not spread to other places outside of electromagnetism.

[0060] (2) When analyzing electromagnetism based on special relativity, it is customary to choose charge 2 as the reference system (i.e., let v 2 +v 3 = 0), so that charge 2 is only affected by the electric field of the moving charge, and the electric field of the moving charge can be calculated by relativity. The result is the same as v 3 It doesn't matter, but v 3 The effect is limited to the process of coordinate transformation.

[0061] So from this point of view, the conclusion that "the acceleration of an object is related to the velocity of the reference frame" is spread to all dynamics, but it is separated from the conclusion that "each inertial reference frame is equal" by complex coordinate system transformations.

[0062] Therefore, in the existing methods, electromagnetics retains v 1 v 2 term; Newtonian mechanics and relativity both tend to eliminate v by coordinate translation 1 v 2 The advantage of this is that v 3 It only appears in the process of coordinate transformation or electromagnetic "coordination", but not in dynamic equations (such as F=ma).

[0063] 1013. Speed ​​cross product modeling submodule

[0064] Keep v 1 v 2 The reason for the child.

[0065] In electromagnetism, v is preserved 1 v 2 sub-term and attribute this term to "magnetism". This is beneficial. The coordinate translation method can only eliminate one velocity in the system at most. When there are multiple (n) moving objects with different speeds in the system (there are v 1 , v 2 ……v n ), at most one speed can be eliminated, and the remaining (n-1) speeds cannot be eliminated, and the interference terms between them must exist. Multiple translations may be able to eliminate multiple speed terms, but the "coordination" between the results of each translation is bound to be very complicated. Therefore, it is necessary to find a way to deal with the interference terms.

[0066] The above analysis shows that the various methods of "isolating" the two contradictory views of "whether acceleration is related to the reference frame velocity" in electromagnetism seem incomplete. Special relativity also shows that phenomena similar to "magnetism" will not only appear in electromagnetism, but also in all moving objects.

[0067] Let's repeat the above analysis from another angle as follows. In the above analysis, one of the key issues is that the dynamic equation (such as F=ma) and the reference frame velocity v 3 More specifically, the acceleration a and the reference frame velocity v 3 Are these two quantities independent (orthogonal or independent). However, the above analysis shows that when there are multiple charged objects moving at different speeds, the expression of their acceleration must include the reference frame velocity v 3 Therefore, it is necessary to analyze the correlation between acceleration and reference frame velocity.

[0068] A rough understanding is that velocity is the first-order derivative of the position of an object, and acceleration is the second-order derivative of the position of an object. In physics, there are also higher-order derivatives of position, such as the third order, but higher-order derivatives are not commonly used. Formally, this is somewhat similar to the mathematical polynomial expansion of a Taylor series for a system (such as the length of the motion path of an object in the system):

[0069] f(x)=f(a)+f'(a)(xa)+f''(a)(xa)^2 / 2!+f'''(a)(xa)^3 / 3!+...+f(n)(a)(xa)^n / n!+...

[0070] However, the Taylor series expansion in mathematics is not an orthogonal series expansion, and the two sub-terms in the nth term (nth power or nth derivative) cannot be used as an orthogonal basis. In contrast, when a system is expanded by a Fourier series polynomial, its basis functions are orthogonal.

[0071] In other words, if the mechanical system is understood as a series expansion of a high-dimensional system:

[0072] 1. Methods such as velocity and acceleration are similar to Taylor series expansion. Velocity and acceleration are generally not orthogonal or independent.

[0073] 2. The wave function or Hilbert space is similar to the Fourier expansion, and the basis functions are orthogonal to each other.

[0074] Under this understanding, the inertial reference frame is equal and can be understood as:

[0075] 1. By coordinate translation, a certain velocity in the system can be reduced to 0. When the system contains only two objects (two velocities), the cross term v1 v 2 , quadratic term v 1 ^2 will be eliminated.

[0076] 2. When the system contains three or more objects with different speeds, all cross terms v cannot be eliminated by translation. 1 v 2 , and v3 will also appear in the cross term through speed synthesis.

[0077] 3. Under general linear transformation, v 3 May appear in various terms (such as velocity terms, acceleration terms, etc.).

[0078] Therefore, "inertial reference frames are equal" indicates that there is only a weak "independence" between dynamics and kinematics, which is much less than linear independency. Therefore, it is necessary to keep v in the dynamic equations. 1 v 2 item.

[0079] This module has two main focuses:

[0080] 1. Recognize that in a high-dimensional system, the force (or acceleration) and the reference frame velocity are related, and the correlation cannot be eliminated by coordinate translation. The above analysis based on physical phenomena is complex and abstract, but from a mathematical point of view, this problem is very simple and intuitive. In 3D space, at most 3 mutually orthogonal straight coordinates can be found. To complete the modeling of high-dimensional objects in 3D space and require the coordinates to be orthogonal, then only non-straight coordinates such as trigonometric function coordinates can be selected.

[0081] 2. Model the interference term energy as an independent motion orthogonal to other dimensions. Model the high-dimensional system, especially the velocity cross product terms, in a trigonometric function coordinate system or other periodic function coordinate system.

[0082] The above analysis leads to the conclusion that the velocity cross product term is retained, but it is not processed in a flat coordinate system, but it is projected into a periodic function. This method is consistent with the treatment of magnetic fields in electromagnetism.

[0083] 102. Trigonometric function coordinate system modeling module

[0084] This module is used to model high-dimensional systems in trigonometric coordinate systems. This module is used to process (v 1 +v 2 )^2=v 1 ^2+2v 1 v 2 +v 2 ^2, put the above items v 1 ^2, 2v1 v 2 、v 2 ^2 are mapped to periodic functions.

[0085] 1021. Submodule for converting straight coordinates to triangular coordinates

[0086] In the Earth rotation scenario, v 1 corresponds to the circular motion of the Earth-Moon system around the Sun, v 2 Corresponding to the circular motion of the moon around the earth, intuitively, the periodicity of their motion is greater than the straightness, and it is easy to convert them into periodic functions according to the real physical meaning. But this module says that even if v 1 、v 2 Even if they correspond to very "ideal" straight motions, they must also be converted into periodic functions.

[0087] The problem can be clearly seen by comparing Formula 2 with the de Broglie relation. The left side of the de Broglie relation is the kinetic energy of a standard straight motion, and the right side is the energy of a periodic motion. Formula 2 expands it, and the term on the left side of the de Broglie relation representing the straight motion is also given a period, which means that the entire system needs to be projected into the trigonometric coordinate system. The reason for this is to avoid mixing the straight coordinate system with the trigonometric coordinate system.

[0088] Note the difference between "mixing" and "cross-validation" of the straight coordinate system and the trigonometric coordinate system. "Mixed" means that in one modeling of the system, one part uses the straight coordinate system and the other part uses the trigonometric coordinate system. "Cross-validation" means that the entire system is modeled twice using the straight coordinate system and the trigonometric coordinate system, and then the correspondence between the two models is found. Almost all the work in this module is focused on understanding and dealing with how to avoid "mixing" the two coordinate systems. The following is an explanation based on a specific physical scenario.

[0089] Let's first explain intuitively what this step does for the "mixed" scenario of the straight coordinate system and the trigonometric function coordinate system. 1 +v 2 )^2=v 1 ^2+2v 1 v 2 +v 2 ^2, the previous step explains the v 1 v 2 The energy term corresponds to the necessity of periodic motion in the trigonometric coordinate system; it turns out that v 1 ^2, v 2The energy of these two terms ^2 corresponds to the straight motion in the straight coordinates. Now convert these two terms into periodic motion in the trigonometric coordinate system. In this way, the three terms in the formula are uniformly converted into trigonometric coordinates, which can avoid the uncertainty caused by mixing straight coordinates and trigonometric coordinates. Non-orthogonal (non-vertical) coordinate systems will bring about anomalies such as uncertainty and non-commutation, which have been analyzed and verified in plane geometry and will not be repeated here.

[0090] Corresponding to the embodiment of the earth's rotation, equation 2 is expanded from the de Broglie relation, and the result of the expansion is that periodic information is also added to the straight motion term in the de Broglie relation. The reason for this is intuitively explained below.

[0091] 1022. Missing parameter supplement submodule

[0092] A known characteristic is that more parameters are needed to determine trigonometric coordinates than to determine straight coordinates. Therefore, when converting straight coordinates to trigonometric coordinates, the missing parameters need to be supplemented. On the other hand, the following analysis shows that the missing parameters are the source of uncertainty.

[0093] The left side of the de Broglie relation represents the energy of the particle's straight motion, while the right side represents the energy of the wave, thus linking the particle and wave properties together. However, the result of doing so is the mixing of straight coordinates and trigonometric coordinates. Mixing straight coordinates representing straight motion with trigonometric coordinates representing wave or periodic motion will lead to uncertainty. It can be seen that the de Broglie relation is the source of wave-particle duality and also the source of uncertainty.

[0094] In Formula 2, adding periodic information to the linear motion term actually transforms the motion from linear coordinates to periodic function coordinates (trigonometric function coordinates). This can eliminate the contradiction (consistency or completeness problem, where completeness and certainty have the same meaning) generated during the projection process from high-dimensional space to low-dimensional space.

[0095] In order to analyze the feasibility of this approach, we combined the Compton scattering experiment for analysis. Compton scattering is an experiment used in physics to illustrate the wave-particle duality. This experiment gives the result data under many different conditions, so it is easy to find the law from it.

[0096] As attached Figure 5As shown in the figure, after a beam of light is scattered by the same substance, the scattered light at the same angle has two frequencies (two wavy curves, only the frequency corresponding to the peak value needs to be paid attention to). These two frequencies correspond to the wave and particle properties of light respectively. According to Compton's paper, the two frequencies are generated by the collision of photons with free electrons and electrons bound to atomic nuclei respectively. In other words, if we know which type of electron the photon collides with, we will know whether the photon will show wave or particle properties after the collision.

[0097] Combined with Figure 4 , the wave and particle properties of particle collision are explained as follows. Assume that Figure 4 a. Two rigid balls move in the same direction. Under the joint constraints of energy conservation and momentum conservation, attachment may occur. Figure 4 b. One is that the two balls keep their energy and momentum unchanged and continue to move in their own direction (assuming that the balls do not occupy the space exclusively, so that they can move towards each other like waves); the other is that the two balls bounce off each other. In this case, the energy of the two balls remains unchanged, but the momentum changes greatly (the speed is reversed). The solution with a small change in momentum and a large change in energy is called "quasi-wave" later, corresponding to the following Figure 4 Point A in the figure; the solution with large momentum change and small energy change is called "partial particle property", corresponding to the attached Figure 4 Point B in .

[0098] Further analysis shows that the two frequencies after scattering are two solutions under the constraints of energy conservation and momentum conservation, as shown in the attached figure. Figure 5 b. The solution under the energy conservation constraint corresponds to the points on the ellipse in the figure, while the solution under the momentum conservation constraint corresponds to the quantity on the straight line in the figure. There are two intersection points between the two, corresponding to the two frequencies mentioned above.

[0099] The entire Compton scattering experiment did not show uncertainty. The part of the experiment that showed the relationship between particle properties and momentum conservation is also bound to waves and periodicity. This is different from the de Broglie relation, which involves the relationship between a non-periodic straight motion and a periodic wave, in which the particle property is a straight motion, bound to straight coordinates; the wave property is bound to periodic waves. Compton scattering involves the relationship between two periodic waves. This also shows that uncertainty does not come from particle properties or microscopic scales, but from the mixing of straight coordinates and trigonometric coordinates.

[0100] Straight coordinates can be considered as the limiting case of trigonometric function coordinate sequences, but in reality, limiting cases do not exist. Straight lines are just trigonometric function curves with "large periods". By assigning periodic parameters to "straight lines", we can convert "straight lines" into trigonometric function curves. The periodic parameters can be obtained through more measurements.

[0101] Referring to the Compton scattering experiment, there is reason to believe that mapping the entire high-dimensional system into an orthogonal trigonometric function coordinate system can eliminate most of the uncertainties (not completely, because it is ultimately a mapping from high dimensions to low dimensions). To complete the high-dimensional mapping operation, more measurements are needed, especially cross-measurements (multiple measurements with slightly changed conditions, rather than completely consistent conditions), to obtain more system parameters. This is the implementation method for completing high-dimensional mapping.

[0102] In this specification, the cross measurement between straight coordinates and trigonometric coordinates is used as an example for explanation. However, it is obvious that cross measurement can also be formed between multiple straight coordinate system models with different conditions or between multiple trigonometric coordinate system models with different conditions. Or the trigonometric coordinate system can be generalized to other periodic function coordinate systems, which can also form cross measurement.

[0103] 103. Cross-validation module

[0104] This module completes the correspondence between the straight coordinate system model and the trigonometric function coordinate system model. This module is used to process the form (v 1 +v 2 )^2=v 1 ^2+2v 1 v 2 +v 2 ^2, where v 1 ^2 items, v 2 ^2 These two items, whether they are more flat or more periodic, can find intuitive physical pictures, and it is convenient to complete the correspondence between the two models. For example, in the Earth's rotation period scenario, v 1 represents the Earth-Moon system's revolution around the Sun, v 2 represents the Moon's revolution around the Earth, and both motions are easy to model in both coordinate systems.

[0105] 1031. Residual Analysis Submodule

[0106] The interference term v among the above items 1 v 2 , corresponds to abstract concepts such as interference, magnetic field, and relativistic effects. Its modeling and cross-validation need to be analyzed in combination with specific physical scenarios. In particular, this term represents the "remainder" that cannot be fully processed in a single coordinate system and needs to be supplemented with the measurement and calculation results of another coordinate system. For example, in the Earth's rotation scenario, the interference term v 1 v 2 It represents the "locked" relationship between the movements of various dimensions in the trigonometric coordinate system achieved through gravity. However, the dimensions should be orthogonal and independent, and the constraints connecting the dimensions cannot be expressed in the trigonometric coordinate system.

[0107] In order to achieve the goal of parameter supplementation through cross-measurement, it is necessary to find the "common parameters" between the two models, that is, the parameters that remain unchanged during the model transformation process. An assumption included here is that when the main items of the two models correspond well, the remaining residual items of the two models can also correspond well, so they can share some residual item parameters.

[0108] However, it is not fixed which parameter remains unchanged during the model transformation process. In reference 1, the model transformation is completed by replacing the "atomic action" in the de Broglie relation with the real action of ordinary objects, but this transformation process is not intuitive.

[0109] In the prior art, the "Energy Equipartition Theorem" is a theorem in thermodynamics that describes the constraint relationship between two dimensions, and the "Action" is a parameter that remains unchanged during the conversion of the quantum wave-particle model. Both concepts are close to the goal of this module, but it can also be seen that they are significantly different from the relationship between energy and frequency in the Earth's rotation cycle scenario:

[0110] 1. The "Energy Equipartition Theorem" in thermodynamics is the result of combining momentum and frequency, while in the Earth's rotation scenario, it is the result of combining energy and frequency. Figure 7 shown.

[0111] 2. In the quantum wave-particle model conversion process (E=hν), energy and frequency are directly proportional, and the greater the energy, the greater the frequency. In formula 2, energy and frequency are inversely proportional, and the greater the energy, the smaller the frequency.

[0112] Combining the above two scenarios, the relationship between energy and frequency in the Earth's rotation period scenario, that is, the equations on the left and right sides of equation 2, is explained:

[0113] 1. Based on the energy equipartition theorem, we can expand it and get the action equipartition.

[0114] 2. By analogy with electromagnetic waves, the advancing direction is perpendicular to the lines of equal action, resulting in equal distribution of action.

[0115] It should be noted that although the "actual movement path of the object" in the Earth rotation scenario and the quantum scenario are both "the path of least action", the energy-frequency relationship in the two scenarios is different. The product of energy and frequency in the Earth rotation period scenario (Eν, i.e. the left or right term of Equation 2) is a constant; this is significantly different from the quantum action (h = E / ν) being a constant. The reason for this difference is that the constraints of the two scenarios are different. The constraint condition of the Earth rotation scenario is the shortest path (the center of mass of the Earth and the Moon moves in a quasi-uniform straight line), while the constraint condition in the quantum scenario (the refraction of light scenario) is the shortest time. Combined with the attached Figure 6Instructions are as follows.

[0116] In the refraction of light, it is the minimum action line under the constraint of constant frequency. The frequency of light is determined by the frequency of the light source and remains unchanged during the propagation process. In a less strict intuitive understanding, if the frequency of light remains unchanged, the energy remains unchanged. Since the action is equal to energy multiplied by time, the path of light is both the shortest time path and the minimum action path under the constraint of constant frequency.

[0117] During the rotation of the Earth, the energy of the interference term of the Moon's revolution is added to the two motions of the Moon's revolution and the Earth's rotation. The center of mass of the Earth and the Moon performs quasi-uniform linear motion, and a straight line is the shortest path between two points, so it is modeled as a minimum action path under the shortest path constraint. The generatrix of the cycloids corresponding to the two (the motion trajectory of the axis of the wheel line) is the same. From a dimensional point of view, the action of this scenario should have been a quantity similar to Eνs (where s represents the path length), but because of the shortest path constraint, the path length is a constant and is therefore omitted in the formula. It can be concluded that energy and frequency are inversely proportional. Below, Eν in this scenario and E / ν in the quantum scenario are referred to as "energy-frequency relationship quantities", or "actions under constraints", or simply referred to as "actions". As shown in the attached Figure 6 shown.

[0118] Attachment Figure 6 Some additional explanations. Figure 6 In a and b, the "wheel line" (also known as the cycloid, the brachistodes line) represents the "path of least action". Intuitively, action equals energy multiplied by time, and in the brachistodes line and light refraction scenes, the total energy is fixed, so the minimum action is equal to the shortest time. In the model conversion of the earth rotation scene (see Appendix Figure 6 a), the constraint is not the shortest time, but the shortest path. However, the cycloid is still used in the figure.

[0119] 1032. Equi-action line analysis submodule

[0120] The forward direction is perpendicular to the equal action line. The forward direction is the minimum action line (which may be the minimum action under the shortest time and shortest path constraints).

[0121] An important conclusion in optics is that under the action of electromagnetic force, the direction of light travels perpendicular to the line of equal action. Figure 4 As shown in the figure, light a and light b interact through electromagnetic force. When refracted in different media, the forward speeds of light a and light b are different, but the frequency remains the same. In this case, the forward direction is perpendicular to the iso-action line, even in the refractive interface.

[0122] Similar, as attached Figure 6As shown in Figure 1, the moon and the earth interact through gravity. The moon revolves around the earth under the gravitational force of the earth and the moon, and the earth rotates on its own under the gravitational force of the earth and the moon. However, the frequencies of the periodic motion (the moon's revolution around the earth and the earth's rotation) are different. This is similar to light moving forward while also performing periodic motion.

[0123] Their forward speeds of orbiting the sun, similar to straight motion, are the same, and are approximately equal to the speed of the center of mass of the Earth-Moon system orbiting the sun. If the direction of the orbiting sun is regarded as the "forward direction", then if the Earth-Moon motion also has the rule that the forward direction is perpendicular to the line of equal action, then the relationship between their motion frequency and energy will be as shown in Equation 2.

[0124] It should be noted that "the direction of light is perpendicular to the lines of equal action" and the "law of refraction of light" can be deduced from each other. If it is assumed that the action of the photon before and after refraction is the same, and the action of different photons on the same line of equal action is the same, then the quantitative refraction of light can be derived. Like the law of refraction of light, the direction of light is perpendicular to the lines of equal action is a summarized rule, not inferred. Similarly, the direction of the Earth-Moon system is perpendicular to the lines of equal action is also a conclusion obtained by analogy, not inference.

[0125] The relationship between the energy and frequency of the Earth's rotation and the Moon's revolution around the Earth can be described by "equal action" or "equal action". In Reference 1, Equation 2 is obtained by expanding the de Broglie relation, which actually adds periodic information to the energy term on the left side of the equation representing the straight motion to obtain the "equal action" relation. In this module, it is directly obtained by analogy with the "equal action line" principle in the refraction process of light. It should be noted that the de Broglie relation itself is also derived by analogy with the refraction of light. Therefore, there is a comparable consistency between the refraction of light, the de Broglie relation, and the equal action of the Earth-Moon system.

[0126] In the previous description, the motions of the various dimensions of the system are mutually orthogonal, so the dimensions should be mathematically independent. For example, the rotation of the earth and the revolution of the moon around the earth are mapped to two independent dimensions, so they should be independent of each other. However, these two are dual motions generated by the same earth-moon gravity, and are connected by equipartition of action in the description of this module. Similarly, the electric field and magnetic field in electromagnetic waves are considered to be perpendicular to each other, but they are "coordinated" with each other through Maxwell's equations; different rays of the same beam of light are considered to be independent and divisible, but they are connected by equal action lines even when passing through a refractive medium during the forward movement. By analogy, it can be found that this module should not be considered to be contradictory to the previous module.

[0127] On the contrary, this step should be considered as realizing the "cross-measurement" or "cross-validation" between the trigonometric coordinate system and the straight coordinate system, and is an important step to reduce the error generated in the projection process of high-dimensional space into low-dimensional space. Specifically for the scenario of the Earth's rotation period, the Earth's rotation, the Moon's revolution around the Earth, and the Earth-Moon system's revolution around the Sun are projected into the three dimensions of the trigonometric coordinates, and they are considered to be independent of each other in the trigonometric coordinates. However, these three movements are obviously "locked" by gravity, and this relationship cannot be displayed at all in the trigonometric coordinates. Therefore, it is necessary to model the "locking" relationship achieved by gravity in the straight coordinates, and then project the modeling results back into the trigonometric coordinates to achieve the purpose of reducing errors. This step is similar to when taking a photo of a three-dimensional object, there are always some parts that are blocked on the "back"; if you can take another photo at a different angle, the two photos complement each other, which can reduce the chance of being blocked.

[0128] 1033. Energy averaging extension analysis submodule

[0129] Derive the equipartition of action from the equipartition of energy.

[0130] A principle similar to "equal distribution of action" is the "equal distribution of energy" principle in thermodynamics, and action equals energy multiplied by time, so "equal distribution of action" seems to be an extension of "equal distribution of energy". Let's try to deduce the above relationship between energy and frequency from the perspective of "equal distribution of energy".

[0131] Energy equipartition, or thermal equilibrium, is a common physical phenomenon. It means that when a system is in thermal equilibrium, all dimensions of the system have the same energy.

[0132] The energy equipartition of a thermodynamic system is actually the equipartition of the product of momentum and frequency, and its reasoning process is introduced in thermodynamics. Hereinafter, the thermodynamic energy equipartition is referred to as the system being balanced under the conditions of momentum and frequency. Correspondingly, the Earth-Moon system is balanced under the conditions of energy and frequency. It can be seen that the difference between the two is that the equilibrium condition is changed from momentum to energy. Therefore, it is necessary to analyze the reason why the equilibrium condition is changed from momentum to energy.

[0133] In fact, the above two equilibrium conditions are similar to the wave-particle duality discussed above, and both meet the conditions of conservation of energy and conservation of momentum. When the mass difference of the interacting objects is small, the momentum condition is in a more prominent position; and when the mass difference of the interacting objects is large, the energy condition is in a more prominent position. In the interaction between the Earth and the Moon through gravity, the mass of the Earth is much greater than the mass of the Moon, so the energy condition is manifested; further, the energy condition is combined with the frequency condition to obtain the equipartition of action. Similar discussions of momentum conditions and energy conditions have been discussed above, and will not be expanded here.

[0134] Here we will use an intuitive but not rigorous method to explain what "equal distribution of action" means.

[0135] The Earth's rotation and the Moon's revolution around the Earth are both dual motions produced by the gravitational forces of the Earth and the Moon, so there is a kind of "speed lock" between these two motions.

[0136] Intuitively, the "velocity lock" generated by the interaction between objects can be classified according to the order of velocity.

[0137] 1. When two objects are connected by a rigid body, or there is a very large friction between the two objects, the two objects are bound together and have exactly the same speed, which is intuitively understood as "first-order locking of speed", which is analogous to the same length of two objects in geometry.

[0138] 2. When a group of particles reach thermal equilibrium through thermal radiation, they have the same kinetic energy, for example, the same translational kinetic energy 1 / 2mv^2, where the particle mass m can vary, and the kinetic energy can be in different forms such as translational kinetic energy or rotational kinetic energy. This can be intuitively understood as "second-order locking of velocity", which is similar to two geometric objects with the same area but variable length and width.

[0139] 3. In the case of quantum interactions such as photons, the main manifestation is action locking, that is, the particle itself has the same action before and after the interaction, and between the particle and other particles around it. The dimension of action is energy multiplied by time, for example, 1 / 2mv^2*t. Although there is no v^3 in the formula, since it is an extension of the v^2 related formula, it is intuitively understood here as "third-order locking of velocity", which is similar to the two objects in geometry having the same volume but variable length, width and height.

[0140] Therefore, it is a common phenomenon that objects produce "third-order locking of velocities" during their interactions, especially when particles interact through electromagnetic force. If it is assumed that the Earth and the Moon produce "third-order locking of velocities" when they interact through the Earth-Moon gravitational force, the theoretical derivation results are consistent with the actual measured values; on the contrary, if it is assumed that "first-order locking of velocities" occurs between the Earth and the Moon, the theoretical derivation results are inconsistent with the actual measured values, and some additional, unverifiable assumptions need to be introduced.

[0141] 104. Description of the mathematical assumptions used

[0142] For ease of understanding, the mathematical assumptions and viewpoints used in the above modules are summarized as follows:

[0143] 1. Complex motion systems of multiple objects require a high-dimensional coordinate system to describe. The method of constructing a high-dimensional coordinate system is generally achieved in two-dimensional or three-dimensional space through the method of polynomial expansion, and the basis of the polynomial expansion is the high-dimensional coordinate system. Polynomial expansion is generally a Taylor expansion based on derivatives and powers, or a Fourier expansion based on trigonometric functions. These expanded coordinates are either non-straight or non-orthogonal. For example, it is well known that a three-dimensional model with straight and orthogonal coordinates cannot be constructed on a two-dimensional plane. However, different polynomial expansions can form "cross measurements" with each other, which can be used to reduce errors caused by projection.

[0144] 2. The description of high-dimensional systems based on physical quantities such as velocity v (first derivative of position), acceleration a (second derivative of position), and energy (second power of velocity) is similar to the Taylor expansion in mathematics, and its expansion coordinates are not orthogonal. This will lead to the correlation between velocity and acceleration in the Taylor expansion model of high-dimensional systems.

[0145] 3. The cross product represents a certain "correlation" or "non-orthogonality" between two quantities. The magnetic field and relativistic effects in physics originate from the terms containing the v1v2 cross product. The root cause can be attributed to the non-orthogonality of the coordinates used, rather than the physical effects such as the invariance of the speed of light or the contraction of the scale. This non-orthogonality is generated when a high dimension is projected into a low dimension.

[0146] 4. Since the third derivative or more of position is rare in physics, trigonometric coordinate systems such as Fourier expansion are generally introduced when dealing with higher-dimensional systems. This will lead to the mixing of straight coordinates and trigonometric coordinates, which will further lead to errors, uncertainties or incompleteness. The solution is to completely transform the quantities in the original straight coordinate system into the trigonometric coordinate system. BRIEF DESCRIPTION OF THE DRAWINGS

[0147] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for describing the prior art and the embodiments are briefly introduced below.

[0148] Figure 1 It is a flow chart of a device for processing non-orthogonal coordinate system errors in a high-dimensional motion system in an embodiment of the present invention;

[0149] Figure 2 It is a schematic diagram of each submodule;

[0150] Figure 3 It is a schematic diagram of the relationship between magnetic force and reference frame velocity;

[0151] Figure 4 When particles collide, two solutions appear under the joint constraints of energy conservation and momentum conservation, corresponding to partial wave properties and partial particle properties respectively;

[0152] Figure 5 This is a frequency diagram of Compton scattering. The two scattering frequencies correspond to partial wave and partial particle properties respectively;

[0153] Figure 6 This is a schematic diagram of equal action sharing. Under the gravitational force of the Earth and the Moon, the interference terms of the Earth's rotation and the Moon's revolution around the Earth are in an equal action relationship, and the direction of motion of the Earth-Moon system is perpendicular to the equal action line; by analogy, the direction of light's forward motion is also perpendicular to the equal action line when it is refracted;

[0154] Figure 7 Schematic diagram of the comparison between energy equipartition and action equipartition. a is the action equipartition under the conditions of energy and frequency, corresponding to the energy-frequency relationship between the moon's revolution around the earth and the earth's rotation in the earth's rotation scenario; b is the energy equipartition under the conditions of momentum and frequency, corresponding to the thermal equilibrium scenario. DETAILED DESCRIPTION

[0155] The present invention aims to provide a simpler and more intuitive modeling method based on traditional physics for the specific embodiment of "Calculation of Earth's Rotation Period" in Reference 1. The calculation is mainly based on Formula 2, and the calculation process is the same as that described in Reference 1, and will not be repeated here. The differences in the modeling process are described as follows.

[0156] 1. Tidal model

[0157] When modeling the Earth's rotation based on traditional physics, one question that needs to be explained is that if the Earth's rotation is "driven" by the Moon's revolution around the Earth, then why is the period of the Earth's rotation smaller than the period of the Moon's revolution?

[0158] It is generally believed that the influence of the moon's revolution on the earth's rotation is achieved through tidal motion. Therefore, it is necessary to model the earth, the moon and the tides.

[0159] 1. Tidal “Braking” Model

[0160] This is the traditional model of the Earth's rotation. Some seawater or solid objects on the Earth produce tidal bulges under the influence of the Moon, which is similar to being locked by the Moon. The rotation period of these objects tends to be the Moon's revolution period, which is slower than the Earth's rotation period. When the Earth rotates, it rubs against the tidal bulge and gradually slows down. The whole process is similar to the braking of a vehicle, so it is called the braking model.

[0161] Obviously, in the braking model, the effect of tides can only be to gradually slow down the rotation of the Earth. Therefore, a hypothesis that matches it is that in ancient times, the rotation of the Earth was faster than the current rotation, and it gradually slowed down under tidal braking until it was locked by the Moon.

[0162] 2. Double Pendulum Model

[0163] In this model:

[0164] (1) The Earth and the Moon revolve around the Earth-Moon mass center, which is the first pendulum;

[0165] (2) Under the action of the first pendulum, the tidal bulge rotates around the center of the earth. This is the second pendulum.

[0166] The modeling of the entire system is very similar to that of a double pendulum, so it is called a double pendulum model. Based on the experience of the double pendulum, although the second pendulum is driven by the first pendulum, the rotation speed of the second pendulum can be much faster than the first pendulum. However, one issue that needs to be noted is that what drives the Earth's rotation is the "interference energy" of the Moon's revolution around the Earth, that is, the energy corresponding to the speed change; rather than the speed of the Moon's revolution around the Earth itself.

[0167] In addition to explaining why the Earth rotates faster than the Moon revolves, this model can also explain why the Earth's rotation and the Moon's revolution are in the same plane.

[0168] In comparison, the double pendulum model is obviously simpler than the tidal brake model, because the tidal brake model requires the introduction of two additional independent assumptions:

[0169] 1. In order to explain why the Earth rotates and the Moon revolves in the same plane, it is necessary to assume that a long time ago the Earth and the Moon belonged to the same celestial body and had the same rotation amount at that time.

[0170] 2. In order to explain why the Earth rotates faster than the Moon revolves, we need to assume that the Earth's rotation was faster than the Moon's revolution a long time ago, but the two are becoming synchronized.

[0171] 2. Modeling with a straight coordinate system

[0172] Let the speed of the Earth's revolution around the Sun be v 1 , the speed of the moon's revolution around the earth is v 2 , then the energy difference between the moon at perihelion and aphelion is (omitting the coefficient 1 / 2m):

[0173] 1 / 2m (v 1 +v 2 )^2-1 / 2m (v 1 -v 2 )^2=2v 1 v 2

[0174] This is calculated based on the highest and lowest points of the periodic motion, corresponding to half a period (15 days) of the moon's revolution around the earth.

[0175] 3. Trigonometric function coordinate system modeling module

[0176] Because the Earth's rotation, the Moon's revolution around the Earth, and the Earth-Moon system's revolution around the Sun all have obvious periodicity, it is intuitive and convenient to model them in the trigonometric coordinate system, and I will not repeat the description here. The difficulty lies in the fact that the movements of each period will be "locked" to each other through gravity, and as mentioned earlier, this cross-dimensional constraint cannot be directly modeled in the trigonometric coordinate system, but is treated as a "remainder", which will be handled in the next module.

[0177] 4. Cross-validation module

[0178] As mentioned earlier, the goal of this step is to add an "equal action" constraint between the motions in the two dimensions.

[0179] In the previous step, the moon's revolution around the earth was modeled as a straight motion, and then a period was assigned to it, which seems to have gone in a circle. The reason for not directly modeling it as a circular motion to obtain a period is that the periodic motions in the trigonometric coordinates are orthogonal and unrelated. If the moon's revolution around the earth and the earth's rotation are directly modeled as periodic motions, then they belong to two dimensions in the model and there is no connection between them. Their relationship through the gravitational coupling of the earth and the moon is ignored. Therefore, it is necessary to model the moon's revolution around the earth as a straight motion, reflect the gravitational relationship in this model, and then map the gravitational relationship back to the trigonometric coordinates (the earth's rotation).

[0180] A key step in calculating the action in the straight coordinate system model is to add periodic information to the straight motion term. In the model for calculating the Earth's rotation period, the Earth's rotation is modeled as a periodic motion, while the Moon's revolution around the Earth is modeled as a straight motion, so this step is to give the Moon's revolution around the Earth a period.

[0181] The interference term energy describes the "interference" information generated between two straight motion speeds. These two straight motion speeds can be the speeds of two different moving objects in the same reference frame, or the speed of the same object before and after acceleration, etc. The latter corresponds to the scene of the moon's revolution around the earth. The periodic information corresponding to the straight motion should be the time period during which the straight speed changes. Corresponding to the scene of the moon's revolution around the earth, it should be the "time period" between the moon's aphelion and perihelion, that is, 15 days. During this time period, the moon's speed changes from v 1 +v 2 to v 1 -v 2 The change of (the sun is used as the reference system, v 2 refers to the speed of the Moon around the Earth).

[0182] It is also easy to notice that in this scenario, v 2 In fact, it is the change in speed, and v2 / t=a, where a is the average acceleration. That is to say, v 1 v 2 / t is a fixed value. This sub-item is the product of velocity and average acceleration (v 1 a), from the nature of acceleration, it can be seen that this sub-item is indeed independent of the selection of the measurement time period. According to the above algorithm and approximating the sine wave to a triangular wave (approximately uniformly accelerated motion), any time period is taken, as long as the time period does not contain the "peak" of the triangular wave (the time period does not contain acceleration and deceleration at the same time), for example, the time period is taken as 2 days, the calculation result is the same as the above result. The analogy is that "a uniformly changing electric field produces a stable magnetic field". The interference term corresponds to the magnetic field. The magnitude of the magnetic field has nothing to do with the measurement time period. The important thing is that the time period corresponds to the magnitude of the electric field change during the period.

[0183] It is important to explain that in the trigonometric coordinate system, the interference term v 1 v 2 Related 1 its own period (the orbital period of the Earth-Moon system around the Sun is 1 year), and v 2 The period of the moon's revolution around the earth is 1 month, but the interference term v 1 v 2 The period is not any of them. In particular, this period is not the period corresponding to the modeling of the moon's revolution around the earth as a circular motion, that is, it is not 30 days. The above description is consistent with the de Broglie relation. The basis for the derivation of the de Broglie relation is the periodic phenomenon associated with the selection of two coordinate systems with different straight velocities, so the periodic phenomenon is bound to the unidirectional change of the straight velocity.

[0184] By the interference term v 1 v 2 The period is 15 days, and the action of the remainder in the straight coordinate system model can be calculated; then the action is assigned to the trigonometric function coordinate system model, and the period of the earth's rotation can be calculated.

Claims

1. A device for processing non-orthogonal coordinate system errors in a high-dimensional motion system, characterized in that: include: (1) Flat coordinate system modeling module. Model the high-dimensional system based on a flat but non-orthogonal coordinate system, and find the interference terms caused by the projection of the high-dimensional space into the low-dimensional space. The interference terms are expressed as terms containing cross products as remainder terms. (2) Trigonometric function coordinate system modeling module. Based on an orthogonal but non-flat trigonometric coordinate system, a high-dimensional system is modeled to find the remainder that cannot be modeled. The remainder is expressed as a quantity that contradicts the coordinate orthogonality assumption and represents the constraints between dimensions. (3) Cross-validation module. Find out the parameters that remain unchanged when the above two models are transformed, and assign the parameters about the remainder calculated or measured in one model to the other model to improve the parameters of the other model.

2. The device according to claim 1, characterized in that The interference term may be a term containing the cross product of two velocities. Assuming that there are two or more velocities in the system, the source of the velocities may be one of the following: (1) Select different coordinate reference systems in the system and measure the speed of the same subsystem in different coordinate reference systems to obtain multiple speeds. (2) Select the same reference frame and measure the speeds of multiple different subsystems in the system. (3) For a subsystem with acceleration, measure the velocity of the subsystem before and after acceleration.

3. The device according to claim 1, characterized in that The parameters that remain unchanged when the two models are transformed can be action quantities or energy-frequency relationship quantities, which can be obtained by the following method: (1) Add a time parameter to the above term containing the cross product of two velocities. When the two velocities are the velocities of an object with acceleration before and after acceleration, the time parameter is the time period during the acceleration process.

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