D'Alembert's principle demonstrator based on double-axis floating sphere

Abstract

The application relates to a device for demonstrating Jarnik's theorem based on a double-shaft suspension ball, which comprises a base, a suspension balancer, a suspension ball and a system controller; the suspension ball comprises a spherical shell and a double-shaft overturning balancer arranged in the spherical shell; the double-shaft overturning balancer comprises a first through shaft, a second through shaft and a balance weight; the two ends of the first through shaft and the two ends of the second through shaft are respectively penetrated and fixed on the spherical shell, and the intersection point of the first through shaft and the second through shaft is located at the ball center of the spherical shell; the balance weight comprises three parts which are the same in structure and size, each part is connected with the inner wall of the spherical shell, the center points of the three parts connected with the inner wall of the spherical shell form an equilateral triangle, the axis line of the second through shaft coincides with a median line of the equilateral triangle, and the first through shaft is perpendicular to the plane where the equilateral triangle is located. The application simplifies the device for demonstration, reduces the observation difficulty and improves the demonstration effect.

Description

Technical Field

[0001] This invention relates to a device for demonstrating physical theorems, specifically a device for demonstrating Jacques' theorem based on a biaxially suspended sphere. Background Technology

[0002] CN 116030690 A is an earlier patent application of the applicant, entitled: A Demonstration Device for Dzhanibekov's Theorem in a Non-Weightless State. This demonstration device includes a base, a levitation balancer, a levitation ball, and a system controller. Through the cooperation of the levitation balancer and the system controller, this invention enables the levitation ball to achieve a stable magnetic levitation state. Because the levitation ball possesses the triaxial structure required for Dzhanibekov's theorem, it can generate three different moments of inertia (large, medium, and small), thus realizing the demonstration and observation of Dzhanibekov's theorem in a non-weightless state. This invention utilizes magnetic levitation technology to create a virtual, localized weightless environment, combined with a levitation ball with a unique triaxial structure, forming a demonstration device that can demonstrate Dzhanibekov's theorem in a suspended state. Through the demonstration of this device, Dzhanibekov's theorem, which is normally difficult to observe and demonstrate, can be directly observed, displayed, and taught in a long-term, interactive manner within the natural gravity environment of the ground, thus facilitating the observer's understanding and achieving a good popular science effect.

[0003] The prior patent application discloses two different structures for a levitating sphere: The first structure includes a spherical shell and three shafts of different diameters disposed within it. The centerlines of the three shafts intersect perpendicularly to each other, with the intersection point located at the center of the spherical shell. The ends of the three shafts are attached to the inner wall of the spherical shell, and each shaft end is connected to a handle extending out of the spherical shell, thus forming a levitating sphere with three solid shafts. The second structure includes a spherical shell and a spherical core disposed within it. The spherical surface of the core is attached to the inner surface of the shell. Three through-holes with different inner diameters are formed in the core, and the centerlines of these holes intersect perpendicularly to each other, with the intersection point located at the center of the core, thus forming a levitating sphere with three hollow shafts.

[0004] A suspended sphere formed by a solid or hollow triaxial structure has two stable states (the first and third principal axes) and one unstable state (the central second principal axis). This results in redundancy in the stable state of the demonstration device and makes the structure relatively complex. Unless explicitly marked on the sphere, it's difficult to distinguish whether the sphere is rotating in a stable state under the first or third principal axis. In fact, for the demonstration of Dzhanibekov's theorem, the focus is more on the effect of the unstable flipping motion under the second principal axis. If the two stable states could be reduced to one, ultimately retaining only one stable state and one unstable state, the demonstration device would be simplified, the observation difficulty reduced, and the demonstration effect improved. Summary of the Invention

[0005] The purpose of this invention is to provide a Jacques' theorem demonstration device based on a biaxial suspended sphere, so as to solve the problem of steady-state redundancy in the Jacques' theorem demonstration device caused by the suspension sphere with a triaxial structure.

[0006] The objective of this invention is achieved as follows:

[0007] A demonstration device for Jahr's theorem based on a biaxially levitated sphere includes a base, a levitation balancer, a levitated sphere, and a system controller. The levitated sphere comprises a spherical shell made of magnetically conductive material and a biaxially levitated balancer made of non-magnetically conductive material disposed within the spherical shell. The biaxially levitated balancer includes a first through shaft and a second through shaft that are perpendicularly connected to each other, and a counterweight for achieving levitation and balance. The two ends of the first through shaft and the two ends of the second through shaft extend out and are fixed to the spherical shell, respectively, and the intersection of the first through shaft and the second through shaft is located at the center of the spherical shell. The counterweight comprises three identical parts of the same structure and size, each part being in contact with the inner wall of the spherical shell. The center points of the three parts in contact with the inner wall of the spherical shell form an equilateral triangle. The axis of the second through shaft coincides with one of the perpendicular bisectors of the equilateral triangle, and the first through shaft is perpendicular to the plane containing the equilateral triangle.

[0008] Furthermore, the counterweight is a star-shaped structure composed of three strips arranged in a centrally symmetrical manner, each segment being a strip; the extended section of each strip is a cylinder, an elliptical cylinder, or a square prism with a rectangular cross-section, and a central through hole is opened along the axis of each strip, through which a second through shaft passes; a central through hole is opened at the center of the plane of the star-shaped structure, through which a first through shaft passes.

[0009] Furthermore, the counterweight consists of three hemispheres, each with a bottom surface that is an arc surface that fits into the inner wall of the spherical shell. A through hole is opened along the axis of each hemisphere, and the second shaft passes through the through hole in one of the hemispheres.

[0010] Furthermore, the two protruding ends of the first through shaft on the spherical shell have the same protruding length, so as to form a set of handles for rotating the suspended ball.

[0011] Furthermore, the two protruding ends of the second through shaft on the spherical shell have the same protruding length, so as to form another set of handles for rotating the suspended ball.

[0012] This invention, through the cooperation of a levitation balancer and a system controller, enables a levitated ball to achieve a stable magnetic levitation state within the space between the base and the levitation balancer. Specifically, the levitated ball can generate two different moments of inertia around two pivot axes. By manipulating the handles at either end of the first or second pivot axis, the levitated ball can be rotated around these axes. This allows for the demonstration and observation of Dzhanibekov's theorem in a non-weightless state. When the levitated ball is in a static, suspended state, rotating the handles on different pivot axes will provide initial rotational momentum, leading to stable rotation. When the levitated ball rotates around the first pivot axis, it maintains a stable rotation; however, when rotating around the second pivot axis, a 180° rotation of the pivot axis, as described by Dzhanibekov's theorem, occurs.

[0013] The dual-axis flipping balancer has a greater weight-to-weight ratio compared to the spherical shell. Thus, on the one hand, the spherical shell allows the suspended ball to levitate; on the other hand, the cooperation between the dual-axis flipping balancer and the first and second through shafts enables the suspended ball to operate under the conditions of Dzhanibekov's theorem, meaning the flipping effect produced by Dzhanibekov's theorem can be achieved through the balancing weights on the spherical shell. Furthermore, the electromagnetic properties of the suspended ball remain constant in any posture within the levitation space of the demonstration device of this invention, and its internal torques are always balanced. Therefore, in a magnetically levitated state without external forces, the suspended ball can remain stationary or rotate at a constant speed.

[0014] This invention changes the triaxial structure of the suspended sphere to a biaxial structure, allowing the Janibekov theorem demonstration device to maintain only one stable state and one unstable state. This provides a more intuitive and clear demonstration of the intrinsic properties of rigid objects during rotation, as described in Janibekov's theorem. This simplifies the structure of the suspended sphere, eliminates the redundancy of stable states present in existing demonstration devices, and is easier to control. The demonstration of Janibekov's theorem is more concise, intuitive, and clear, better showcasing its effectiveness. This invention simplifies the demonstration device, reduces observation difficulty, and enhances the demonstration effect. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the structure of the present invention.

[0016] Figure 2 This is a schematic diagram of the internal structure of the suspended sphere in Example 1.

[0017] Figure 3 This is a schematic diagram of the internal structure of the suspended sphere in Example 2.

[0018] In the diagram: 1. Suspension balancer, 2. Base, 3. Suspension ball, 4. Rotary handle, 5. Arc-shaped bracket, 6. Permanent magnet, 7. Control coil, 8. Position sensor, 9. Spherical shell, 10. Star-shaped structure, 11. First through shaft, 12. Second through shaft, 13. Hemisphere. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0020] Example 1

[0021] like Figure 1 As shown, the demonstration device in this embodiment includes a levitation balancer 1, a base 2, a levitation ball 3, and a system controller. A permanent magnet 6 is positioned at the center of the bottom surface of the levitation balancer 1, and a control coil 7 is wound around the permanent magnet 6. The base 2 is frustum-shaped, and the system controller is built into it; a position sensor 8 is located at the center of the top surface of the base 2. Both the control coil 7 and the position sensor 8 are electrically connected to the system controller installed in the base 2. The position sensor 8 detects the position of the levitation ball 3 and provides the position data to the system controller. The arc-shaped support 5 is a bent rod, with its lower end fixedly connected to the side edge of the base 2 and its upper end fixedly connected to the side edge of the levitation balancer 1, so that the levitation balancer 1 and the base 2 are vertically aligned.

[0022] The levitation balancer 1, base 2, and system controller in the demonstration device of this invention can be implemented using the corresponding structural components in the applicant's prior patent application. The key to this invention lies in the structural design of the levitation ball.

[0023] like Figure 2As shown, the levitation sphere 3 consists of two parts: a spherical shell 9 and a built-in dual-axis tilting balancer. The spherical shell 9 can be made of soft magnetic ferrite, a soft magnetic material with high permeability and high resistivity. The levitation sphere 3 can be formed by two hemispherical shells interlocking together. The spherical shell 9 has identical electromagnetic properties in all directions; it can be attracted by a magnetic field but will not be magnetized, thus enabling the levitation sphere 3 to levitate and stabilize under the control of the levitation balancer 1, and allowing it to rotate freely in all directions. The dual-axis tilting balancer can be made of non-magnetic metals with high specific gravity, such as copper or lead, to avoid affecting the overall magnetic circuit of the levitation sphere.

[0024] like Figure 2 As shown, the dual-axis tilting balancer comprises three components: a first through shaft 11, a second through shaft 12, and a counterweight. The first through shaft 11 and the second through shaft 12 are connected perpendicularly to each other, and the counterweight is used to achieve tilting and balancing.

[0025] Figure 2 In this structure, the counterweight is composed of three identical strip-shaped bodies arranged in a centrally symmetrical configuration to form a star-shaped structure 10. The extended section of each strip-shaped body can be a cylinder, an elliptical cylinder, or a rectangular prism. The outer end of each strip-shaped body is tightly connected to the inner wall of the spherical shell 9, and the center points where the three strip-shaped bodies meet the inner wall of the spherical shell form an equilateral triangle. A central through-hole is formed along the axis of each strip-shaped body, and a second through-shaft 12 passes through one of these central through-holes, aligning its axis with a perpendicular bisector of the equilateral triangle. A central through-hole is formed at the center of the plane of the star-shaped structure, and a first through-shaft 11 passes through this central through-hole, perpendicular to the plane containing the equilateral triangle. The intersection of the first through-shaft 11 and the second through-shaft 12 should be located at the center of the spherical shell 9.

[0026] The two protruding ends of the first through shaft 11 are respectively threaded through and fixed to the spherical shell 9 to form a set of handles for rotating the suspended ball. The two protruding ends of the second through shaft 12 are respectively threaded through and fixed to the spherical shell 9 to form another set of handles for rotating the suspended ball. Furthermore, the protruding lengths of these four protruding ends on the outer surface of the spherical shell 9 are preferably kept the same, so that the suspended ball 3 can be driven to rotate by manual rubbing or mechanical actuation.

[0027] In the suspended sphere 3, the first through axis 11 is equivalent to the first principal axis that can maintain a stable state in Jacques' theorem, and the second through axis 12 is equivalent to the second principal axis that can maintain an unstable state in Jacques' theorem.

[0028] With the suspended ball 3 in a suspended state, it can be rotated by manually or mechanically rotating one of the sets of handles 4. When the suspended ball 3 rotates around a certain axis at a certain speed, the effect shown by Dzhanibekov's theorem can be clearly observed. That is, if the suspended ball 3 rotates around the first axis 11, the moment of inertia of the system is at its maximum, and the suspended ball 3 is in a stable rotational state. If the suspended ball 3 rotates around the second axis 12, the moment of inertia of the suspended ball 3 decreases because the distance between the counterweight and the second axis is relatively small, but it is not at its minimum (the moment of inertia is minimized when the suspended ball 3 rotates around the second axis 12 and all the counterweights are located on the axis of the second axis 12). According to Dzhanibekov's theorem, the suspended ball 3 is in an unstable state in terms of rotational axis at this time, so the phenomenon of the rotational axis formed by the suspended ball 3 repeatedly flipping can be clearly observed. That is, the orientation of the second axis 12 will continuously change by 180°, thus clearly verifying and demonstrating Dzhanibekov's theorem.

[0029] Example 2

[0030] The demonstration device in this embodiment is basically the same as that in Embodiment 1, except that the structure of the suspended ball 3 is different.

[0031] like Figure 3 As shown, the levitation sphere 3 consists of two parts: a spherical shell 9 and a built-in dual-axis tilting balancer. The spherical shell 9 can be made of soft magnetic ferrite material, a soft magnetic material with high permeability and high resistivity. The levitation sphere 3 can be formed by two hemispherical shells interlocking together. The dual-axis tilting balancer can be made of non-magnetic metals with high specific gravity, such as copper or lead, to avoid affecting the overall magnetic circuit of the levitation sphere.

[0032] like Figure 3 As shown, the dual-axis tilting balancer comprises three components: a first through shaft 11, a second through shaft 12, and a counterweight. The first through shaft 11 and the second through shaft 12 are connected perpendicularly to each other, and the counterweight is used to achieve tilting balance.

[0033] Figure 3In this structure, the counterweight comprises three hemispheres 13 made of the same material, with identical structural shapes and geometric dimensions. The bottom surface of each hemisphere is an arc surface that fits into the inner wall of the spherical shell 9, ensuring a tight connection. The center points where the three hemispheres 13 meet the inner wall of the spherical shell form an equilateral triangle. A through-hole is formed along the axis of each hemisphere 13. A second through-shaft 12 passes through the through-hole of one of the hemispheres 13, with its axis coinciding with the perpendicular bisector of the equilateral triangle formed by the center points of the outer ends of the three hemispheres. A first through-shaft 11 and a second through-shaft 12 are perpendicularly connected, with the intersection point located at the center of the spherical shell 9. Furthermore, the plane containing the equilateral triangle formed by the center points of the outer ends of the three hemispheres is perpendicular to the first through-shaft 11.

[0034] The two protruding ends of the first through shaft 11 are respectively threaded through and fixed to the spherical shell 9. The two protruding ends have the same protruding length on the outer surface of the spherical shell 9, forming a set of handles 4 for rotating the suspended ball, so as to drive the suspended ball 3 to rotate by manual twisting or mechanical drive. Both ends of the second through shaft 12 protrude from the spherical shell 9 and are fixedly connected to the spherical shell 9. The two protruding ends of the second through shaft 12 have the same protruding length on the outer surface of the spherical shell 9, forming another set of handles 4 for rotating the suspended ball.

[0035] In the suspended sphere 3, the first through axis 11 is equivalent to the first principal axis that can maintain a stable state in Jacques' theorem, and the second through axis 12 is equivalent to the second principal axis that can maintain an unstable state in Jacques' theorem.

[0036] This embodiment uses three hemispheres as balancing weights, which better demonstrates the flipping effect of the suspended sphere. Because the center of gravity of each hemisphere 13 is closer to the surface of the spherical shell 9, the moment about the center of the sphere is larger, thus making the effect of Dzhanibekov's theorem more obvious.

Claims

1. A demonstration device for Jahr's theorem based on a biaxially levitated sphere, comprising a base, a levitation balancer, a levitated sphere, and a system controller, characterized in that, The levitation sphere comprises a spherical shell made of magnetically conductive material and a dual-axis flipping balancer made of non-magnetically conductive material disposed within the spherical shell. The dual-axis flipping balancer comprises a first through shaft and a second through shaft that are perpendicularly connected to each other, and a counterweight for achieving flipping and balancing. The two ends of the first through shaft and the two ends of the second through shaft extend out and are fixed to the spherical shell, respectively, and the intersection of the first through shaft and the second through shaft is located at the center of the spherical shell. The counterweight comprises three parts with the same structure and size, each part being in contact with the inner wall of the spherical shell. The center points of the three parts in contact with the inner wall of the spherical shell form an equilateral triangle. The axis of the second through shaft coincides with one of the perpendicular bisectors of the equilateral triangle, and the first through shaft is perpendicular to the plane containing the equilateral triangle.

2. The Jahr's theorem demonstration device based on a biaxially suspended sphere according to claim 1, characterized in that, The counterweight is a star-shaped structure composed of three strips arranged in a centrally symmetrical manner. Each part is a strip. The extended section of each strip is a cylinder, an elliptical cylinder, or a square prism with a rectangular cross-section. A central through hole is opened along the axis of each strip, and a second through shaft passes through one of the central through holes. A central through hole is opened at the center of the plane of the star-shaped structure, and a first through shaft passes through the central through hole.

3. The Jahn's theorem demonstration device based on a biaxially suspended sphere according to claim 1, characterized in that, The counterweight consists of three hemispheres, each with a bottom surface that is an arc surface that fits into the inner wall of the spherical shell. A through hole is opened along the axis of each hemisphere, and a second shaft passes through the through hole in one of the hemispheres.

4. The Jahn's theorem demonstration device based on a biaxially suspended sphere according to claim 1, 2, or 3, characterized in that, The first through shaft has two protruding ends on the spherical shell with the same protruding length, so as to form a set of handles for rotating the suspended ball.

5. The Jahn's theorem demonstration device based on a biaxially suspended sphere according to claim 1, 2, or 3, characterized in that, The two protruding ends of the second through shaft on the spherical shell have the same protruding length, so as to form another set of handles for rotating the suspended ball.

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