48 results about "Conductor sag" patented technology

The invention relates to the technical field of computer vision and power equipment detection, in particular to a power transmission line conductor sag intelligent judgment method based on an unmanned aerial vehicle inspection image, which comprises the following steps: S1, identifying a conductor area based on an unmanned aerial vehicle visible light image, and extracting a continuous conductor edge; s2, an insulator string is positioned in a wire area, and a wire hanging point is accurately positioned through gradient direction aggregation analysis; s3, generating a space datum line based on the digital elevation model and the line direction; s4, conducting wire form reconstruction of physical constraint is executed, the fracture edge is connected with the physical characteristics of a conducting wire catenary as constraint, and the reconstructed conducting wire is projected to a datum line vertical plane; and S5, calculating the maximum vertical distance from the projection point to the reference line as a sag value, and dynamically diagnosing abnormality in combination with the environment temperature. Through combination of image processing, deep learning, a physical model and a terrain adaptive technology, the precision and reliability of conductor sag detection can be effectively improved.

The invention discloses a power transmission line operation and maintenance analog simulation system based on a digital twinborn technology, and relates to the technical field of intelligent operation and maintenance and simulation of a power system, and the system comprises a data collection module which is used for collecting real-time operation state data of a power transmission line and establishing a data link, the data comprises meteorological information, current-carrying capacity, temperature, tension and conductor sag multi-source heterogeneous operation state data, the model building and adjusting module is used for building or adjusting virtual simulation model parameters based on the real-time operation state data, and the comparative analysis module is used for analyzing the real-time operation state data. The analysis module is used for carrying out multi-dimensional comparison analysis on the updated virtual simulation model and an actual power transmission line, and comparison dimensions comprise a tension change trend, wire vibration response and thermal stability distribution; according to the power transmission line operation and maintenance analog simulation system based on the digital twinborn technology, the automation, intelligence and scientization levels of power transmission line operation and maintenance management are improved.

The invention discloses a power transmission conductor sag measurement method and device and a computer program product, and the method comprises the steps: S1, carrying out the cruise sampling along a power transmission line, and obtaining the laser point cloud data corresponding to a power transmission conductor in the power transmission line; s2, carrying out preprocessing operation on the laser point cloud data; s3, based on the preprocessed laser point cloud data, extracting a lead skeleton area through density field estimation and a space attention mechanism; s4, constructing a flexible catenary morphological model on the basis of the lead skeleton area and in combination with physical constraints of the power transmission lead; and S5, calculating the sag value of the transmission conductor according to the flexible catenary form model. According to the method, the stability of key point position extraction is greatly improved, and the accuracy of sag calculation in different operation states, topographic conditions and meteorological environments is further remarkably improved.

The invention discloses a power transmission line icing sag thickness measurement method and system based on machine vision, and belongs to the technical field of visual observation, and the method comprises the steps: obtaining a first power transmission line image and a second power transmission line image, and obtaining the point cloud data of a center line of a wire according to the second power transmission line image; catenary fitting is carried out based on the conductor center line point cloud data to obtain a conductor catenary model, and sag estimation is carried out according to the conductor catenary model to obtain conductor sag distribution data; performing icing area extraction on the first power transmission line image, and performing icing thickness inversion mapping in combination with the second power transmission line image to obtain conductor icing thickness distribution data; and performing correlation fitting on the conductor sag distribution data and the conductor icing thickness distribution data to obtain a fitting function, and obtaining an icing sag thickness distribution increment based on the fitting function to obtain the icing sag thickness. The technical problem that the accuracy of the icing sag thickness is low due to the fact that the dynamic coupling relation between the icing thickness and the conductor sag is not considered in the prior art is solved.

The invention discloses a power transmission line multi-mode cooperative sensing method, a mechanical intrusion early warning method and system and a storage medium, and the sensing method comprises the steps: constructing a reference coordinate system, and projecting multi-source data into the reference coordinate system; calling a tension-length coupling correction operator, and carrying out static equilibrium iteration solution on the design span to obtain a three-dimensional conductor sag physical prior curve; inputting the conductor sag physical prior curve and a historical curve in a sliding window of a preset period into a space-time continuous network, and outputting a conductor continuous sag curve in a span range; the method comprises the following steps: respectively cutting interest areas in a visible light image frame and a 4D three-coordinate radio frequency radar frame by taking plane projection of a conductor continuous sag curve as guidance, respectively extracting conductor optical anchor points and conductor radar candidate points, and generating a conductor fine three-dimensional point array in a span range through a medium radian conservation progressive registration operator; according to the invention, centimeter-level precision sensing can be maintained under extreme high-low temperature and complex load conditions.

The invention discloses a Beidou-based three-dimensional curve reconstruction and sag calculation method for a power transmission conductor, particularly relates to the technical field of space measurement and state perception of a power transmission line, and aims to solve the problems that in existing conductor sag measurement, a three-dimensional space form is easily simplified into a plane relation; problems of insufficient lead real track expression under a complex channel, difficult elimination of a local mixed point column, difficult stable recovery of a continuous curve, and deviation of a sag calculation result from a real clearance position are solved. The method comprises the following steps: acquiring coordinates of Beidou observation points and coordinates of hanging points at two ends, establishing a span coordinate system, forming space contour data, dividing a local observation section and identifying a target span lead body point column, further constructing a reserved observation point set, reconstructing a target lead three-dimensional curve, and calculating vertical difference values at longitudinal positions based on hanging point connecting lines. And finishing the conductor sag calculation of the target gear.

This invention relates to a measurement method for crossing lines in overhead transmission lines, comprising the following steps: collecting geographical data, meteorological data, and parameter data of the area where the crossing line is located, and preprocessing the data; calculating the conductor sag of the crossing line based on the meteorological data and parameter data, and calculating the conductor height based on the conductor sag; calculating the initial net distance of the crossing line based on the conductor height; determining the structure type of the crossing through the geographical data of the area where the crossing line is located, and correcting the initial net distance of the crossing line by setting a corresponding structure correction value according to the structure type, thereby obtaining the final net distance of the crossing line.

The invention belongs to the field of engineering safety detection, and particularly relates to a power transmission line hidden danger detection method and device based on Beidou RTK positioning and image videos. The method comprises the following steps: acquiring an elevation coordinate m1 of a base station of a power transmission line tower, acquiring an elevation coordinate m2 of a lowest point of a conductor sag, acquiring an elevation coordinate m3 of a highest point of a suspension arm of a construction vehicle, calibrating the elevation coordinates m2 and m3 by taking the elevation coordinate m1 as a reference, and respectively calculating corresponding distances to the ground based on the elevation coordinates, the relative distance delta L between the lowest point of the conductor sag and the highest point of the lifting arm of the construction vehicle is further calculated, judgment is conducted based on the corresponding safety distance required by the overhead transmission line design specification standard, when delta L is smaller than or equal to L safety, construction is stopped, and the distance between the conductor sag and the highest point of the lifting arm can be more accurately detected through the method.

The invention discloses a local adjustment method and system for electric transmission line tower arrangement, belongs to the technical field of electric transmission line design, and aims to solve the problems of local violation, high global optimization cost, lack of a self-adaptive repair strategy and dependence on experience decision in traditional manual arrangement. The method comprises the following steps: firstly, carrying out conductor sag fitting and comprehensive checking of sag, ground clearance, crossing and windage yaw on a tower arrangement scheme; recognizing a violation tower position according to a result, and determining a local repair section; then generating candidate repairing actions such as tower moving, tower height increasing and tower inserting; then constructing a multi-objective optimization model, quantifying the repair cost and sequencing the actions; and finally, executing the action according to the priority, and iteratively checking until the hard constraint is met. The method focuses on local repair, reduces the cost, improves the efficiency, adapts to multiple voltage grades and complex terrains, and provides intelligent support for pole tower arrangement design.

The invention discloses an acceleration sensor sampling rate determination method and device for a power transmission line modal test, terminal equipment and a storage medium, and belongs to the field of power systems. The method comprises the following steps: calculating to obtain conductor sag, overhead line horizontal tension and conductor fixed port tension according to obtained conductor physical attributes, span and line point cloud data; constructing a power transmission line modal vibration model according to conductor physical attributes, conductor sag, overhead line horizontal tension and conductor fixed port tension, and solving to obtain conductor inherent frequency; performing a test according to the inherent frequency of the wire and a preset test frequency, and determining the highest modal order and the highest effective frequency; the lower limit of the sampling frequency of the sensor is determined according to the highest effective frequency and the preset safety coefficient, the upper limit of the sampling frequency of the sensor is determined according to the preset number of sampling points and the highest effective frequency, and then the sampling frequency range of the sensor is determined.

The application discloses a power transmission line risk determination method and device and electronic equipment. The method comprises the following steps: dividing the power transmission line into multiple sections; determining the risk influence characteristics of each section, wherein the risk influence characteristics comprise meteorological influence characteristics, terrain characteristics and working condition influence characteristics; performing clustering processing on the multiple sections based on the risk influence characteristics of each section to obtain multiple power transmission line section units; determining the risk probability of each power transmission line section unit according to the risk influence characteristics of each power transmission line section unit, tree line distance, tree growth rate, conductor sag and relative humidity of the environment where the power transmission line is located; and determining the comprehensive risk probability of the power transmission line according to the risk probability of each power transmission line section unit. The application solves the technical problem that the tree barrier discharge probability under complex working conditions cannot be accurately quantified due to the fact that the related risk determination method ignores the spatial heterogeneity of the line and the environmental humidity is not taken into account in the risk assessment.

The invention discloses a conductor sag curve construction method for a heavy-load line, and belongs to the technical field of conductor sag construction, and the method comprises the steps: carrying out the initial parameter setting of an unmanned aerial vehicle according to differentiated environmental conditions, collecting the conductor video of each survey sub-road section, carrying out the iterative optimization of the parameters of the unmanned aerial vehicle, and judging the number of image cutting, and generating a conductor sag analysis image set of each surveying sub-road section, analyzing a conductor sag deviation correction value, generating an ideal conductor sag curve, generating a corrected conductor sag curve, and outputting the ideal conductor sag curve and the corrected conductor sag curve. According to the method, the actual operation condition of the existing line in the target building area can be accurately considered, the ideal and corrected conductor sag curve is finally built, accurate data reference is provided for line design, building and operation maintenance, line faults caused by the conductor sag problem are reduced, unmanned aerial vehicle survey data transmission is dynamically adjusted, and the unmanned aerial vehicle survey data transmission efficiency is improved. And stable and accurate transmission of data is ensured.

The invention provides a power transmission conductor sag monitoring method and device based on digital twinning, and relates to the technical field of sag monitoring, and the method comprises the steps: reading the design data of a power transmission line after obtaining the authorization of a user, and constructing a basic digital twinning model; carrying out sag detection key point identification, and configuring binocular acquisition parameters; power transmission line acquisition is executed, and a binocular image is established; selecting a front view image to carry out local feature analysis, and establishing an adaptive authentication window; pixel matching cost calculation is carried out, and sag detection three-dimensional point cloud reconstruction is carried out; performing depth data extraction, establishing fused depth data of sag detection key points, updating the basic digital twinborn model, and generating a corrected digital twinborn model; dynamic simulation is carried out, and sag abnormity early warning is generated. The method solves the technical problems that the existing sag monitoring method often cannot realize real-time monitoring and is characterized in that high accuracy is difficult to guarantee in a dynamic environment, so that sag abnormity cannot be found in time and early warning cannot be performed.

The application discloses a safety sag calculation method and system for a conductor of a power transmission tower, and the method comprises the following steps: constructing a conductor stress change relationship according to the elastic deformation of the conductor under each control condition and the original length of the conductor; wherein each control condition is set according to preset environmental parameters; determining the conductor tension characteristic under an actual working condition based on the conductor stress change relationship and a preset nonlinear stress change relationship; obtaining a safety sag meeting a predetermined conductor safety requirement according to the conductor tension characteristic, and adjusting the sag of the conductor under the actual working condition according to the safety sag. The application considers the nonlinear characteristics of the conductor when calculating the tension characteristics of the conductor of the power transmission tower under different environments, so that the calculated conductor sag is more accurate and meets the safety requirements of the overhead transmission line, and sufficient data support is provided for effectively evaluating and ensuring the safety of the transmission line.

The invention discloses a power transmission line live working lead sag adjusting device, and relates to the technical field of power transmission lines, the power transmission line live working lead sag adjusting device comprises a fixed base, the bottom of the fixed base is provided with a connection fixing mechanism, the fixed base is provided with a mounting frame, and a plurality of first rib plates are arranged between the mounting frame and the fixed base; a lifting seat mechanism and a lifting adjusting mechanism are arranged on the mounting frame, two symmetrically arranged deflection mounting rod mechanisms are arranged on the mounting frame, a plurality of fixed hanging ring mechanisms are arranged on the deflection mounting rod mechanisms, and two symmetrically arranged deflection adjusting mechanisms are arranged on the lifting seat mechanism; according to the device, mounting connection of the device and an iron tower can be achieved by arranging the connecting and fixing mechanism, the state of the lifting seat mechanism can be adjusted through the lifting adjusting mechanism, and the deflection adjusting mechanism and the elastic connecting mechanism are matched, so that the device is more convenient to use. Therefore, the deflection angle of the deflection mounting rod mechanism is adjusted, and the performance of wire sag adjustment is improved.

The present application belongs to the technical field of aluminum alloy conductor, and particularly relates to a low-creep heat-resistant aluminum alloy conductor and a preparation method thereof. The product of the present application is a novel capacity-increased conductor with high electrical conductivity, high temperature resistance, high strength and low creep, and has the characteristics of low transmission line loss and high operation reliability. After the conductor is treated at high temperature and under large tension, the overall plastic creep elongation of the conductor is eliminated, the influence of the plastic creep elongation of the conductor on stringing and operation is avoided, the designed value of conductor sag at the initial stage of erection is consistent with the actual value. In the process of stringing and operation, the temperature reduction method is no longer used for compensation, the designed value of conductor sag is consistent with the actual value, and the safety hazards and cost increase caused by inaccurate estimated elongation are avoided.

The present invention relates to the technical field of power grid construction, and discloses a conductor support and adjustment device for power grid construction and a method for using the device, comprising a main body, two reinforcing plates fixedly connected to the outer surface of the main body, a support plate fixedly connected to one end of the reinforcing plate away from the main body, and a fixing clamp fixedly connected between the two support plates. The present invention pushes the conductor to move backward during reverse movement and provides a reverse supporting force to jointly maintain the tension stability of the cable, ensuring that no matter how the conductor moves, it can be effectively clamped by the two clamps, so that the cable can be subjected to a certain clamping force and friction between the two adjustment mechanisms, reducing the situation in which the conductor sags or swings when the conductor is pulled during construction due to the action of external wind and its own gravity during construction.

The invention discloses an overhead conductor transient sag monitoring method and device, terminal equipment and a storage medium, and belongs to the technical field of conductor sag monitoring, and the method comprises the steps: obtaining the physical parameters of a to-be-detected conductor, and the current environment parameters of an area where the to-be-detected conductor is located; calculating to obtain the current conductor temperature and knee point temperature; under the condition that the current wire temperature is larger than the knee point temperature, the current wire stress is calculated according to the steel core thermal expansion coefficient, the steel core elastic modulus, the steel core specific load, the initial operation temperature, the wire elastic modulus, the wire thermal expansion coefficient, the initial wire stress, the wire specific load and the current wire temperature; and finally, calculating the current conductor sag according to the current conductor stress. Through implementation of the method and the device, the problems that in the prior art, due to the fact that the overall temperature of the wire is uniformly used for calculating the sag of the wire, the calculated sag of the wire has a large error, and the operation stability of a power system is reduced can be solved.

This invention discloses a method for dynamic modeling of conductor sag driven by BeiDou micro-motion positioning, relating to the field of transmission line data processing. It addresses the problem of unstable dynamic modeling due to insufficient basis for sag state segment continuity in long-term continuous observations. The method involves acquiring the BeiDou micro-motion positioning sequence of multiple conductor observation points within the target conductor span and the coordinate sequences of the two end points, and time-registering them to form micro-motion observation segments. Based on the end point coordinate sequences, the support chord is determined, and the conductor space curve is fitted to generate sag state segments. The normalized arc length surplus of the support chord constraint and the projection migration of the lowest point onto the support chord are calculated and input into the continuity judgment model to obtain the evolution continuity coefficient, thus forming a state transition relationship. The sag state segments are then concatenated according to the state transition relationship to construct a dynamic sag model, and the dynamic sag representation results are output.

The invention discloses a power transmission line tower inclination and conductor sag measuring device, which is characterized in that a laser beam is emitted to a laser receiving plate through conductor end equipment so as to form a light spot on the laser receiving plate, a real-time image of the laser receiving plate is shot, a first real-time coordinate of the center of the light spot in a laser receiving plate coordinate system is calculated based on the real-time image, and then the first real-time coordinate of the center of the light spot in the laser receiving plate coordinate system is calculated; calculating an offset based on the first real-time coordinate and the reference zero position, and calculating an inclination angle of the tower based on the offset; and converting the first real-time coordinate into a first geodetic coordinate and further determining a second geodetic coordinate of the conductor end equipment, and calculating to obtain the conductor sag by utilizing a parabolic equation and based on the geodetic coordinates of the conductor end equipment, the first suspension point and the second suspension point, so that network-dependent measurement technologies such as a network real-time dynamic measurement technology and the like do not need to be used. High-precision positioning and conductor sag measurement in a scene without a network or with a poor network signal are realized, and meanwhile, simultaneous measurement of tower inclination and conductor sag is realized by only using one set of equipment.

This invention discloses an optimization method for calculating conductor sag in all-dielectric self-supporting optical cables based on support vector regression. Addressing the inaccuracies in conductor sag estimation using existing parabolic and catenary methods, this method trains a support vector regression model using extensive historical inspection data, resulting in a precise support vector machine model relating surrounding environmental parameters to sag corrections. In practical applications, relevant surrounding environmental parameters can be obtained from sensors to calculate the sag correction, improving conductor sag estimation accuracy and ensuring optimal line operation.

The application discloses a kind of overhead transmission line wire sag detection devices based on Beidou positioning technology, including hoist module, the hoist module includes storage frame, the outer wall of one side of the storage frame is equipped with connecting block, the front of the clamping block is welded with mounting block, the top of the mounting block is equipped with the pull steel rope of symmetrical arrangement, and pull steel rope is wound on the hoist of fixed in tower pole surface, so that pull steel rope can drive mounting block vertically upwardly moves, the rear wall of the mounting block is equipped with electric push rod one, the front of the connecting plate is inlayed and installed with the electromagnet one of symmetrical arrangement.This application is provided with hoist module, pull steel rope, connecting plate and electromagnet one, first by the attraction of electromagnet one and iron plate two to be fixed in connecting box on connecting plate, and by hoist to pull pull steel rope upward, so that monitoring mobile module is to the horizontal direction monitoring of wire sag, to improve the detection efficiency of wire sag.

This invention provides a method and system for controlling sag during the construction of power transmission lines in mountainous areas. The method includes: acquiring at least one spatial attitude parameter of the overhead conductor within a target span based on non-visual spatial attitude perception; acquiring at least one load state parameter reflecting the current tension state of the conductor based on load inversion (not directly measured); constructing a digital twin mapping, inputting the spatial attitude parameter and load state parameter into a preset digital twin model of conductor mechanical behavior, whereby the digital twin model integrates environmental parameters and performs real-time calculations, outputting the true value of conductor sag at the current construction stage; and dynamically generating and executing an adjustment strategy for conductor tension based on the real-time deviation between the true sag value and the design sag value, until the construction accuracy requirements are met. This invention can improve the quality and efficiency of sag construction for power transmission lines in mountainous areas, ensuring the safe and stable operation of the lines.

The embodiment of the application provides a kind of high temperature big load condition under transmission line conductor sag monitoring method and system, belong to transmission line conductor sag monitoring technical field.The monitoring method includes constructing the model for identifying the suspension point of the conductor sag image of the power pole tower hanging conductor, the vertex and bottom point of the power pole tower;Obtain the real-time image of multiple perspectives of the conductor sag to be monitored at present;The real-time image of the conductor sag is obtained, and the suspension point, fixed point and bottom point of the power pole tower in the real-time image are identified, the available image is filtered out first, then the lowest point of the conductor sag is obtained according to the conductor coordinates in the available image, and the sag value of the conductor can be obtained, which effectively obtains the sag value of the conductor, and the operation is simple, and the measuring efficiency is high.

The invention provides a lead sag monitoring method and system based on Beidou positioning and radar ranging, and is applied to the technical field of operation and maintenance of power transmission lines. The lead sag monitoring method based on Beidou positioning and radar ranging comprises the following steps: acquiring a Beidou positioning data sequence and a radar ranging data sequence of a power transmission line sag; determining the jitter degree of the power transmission line according to the Beidou positioning data sequence; and correcting the radar ranging data sequence according to the jitter degree, and determining sag information of the power transmission line. According to the invention, the Beidou positioning information and the radar ranging information are fused, and the radar ranging data are corrected by using the jitter degree corresponding to the Beidou positioning data, so that the defects of many limited factors and large monitoring result error in the traditional indirect measurement can be avoided, and the monitoring precision of the sag of the power transmission line can be improved. Therefore, on-line monitoring rather than prediction of the sag of the power transmission line is completed, so that stable and high-precision detection of the sag of the power transmission line is realized.

The present application relates to the technical field of power system state monitoring, and provides a power multi-modal data acquisition and processing method and system based on machine learning, which comprises: acquiring ultraviolet images, infrared temperature and sag data of power lines; performing insulator pollution flashover feature fusion and time series prediction through a convolutional neural network and a long short-term memory network, and outputting insulator safety evaluation by using a random forest; performing sag data fusion through Kalman filtering and support vector regression, combining neural network temperature compensation and deep Q network early warning, and outputting sag safety evaluation; and outputting power multi-modal data processing results by comprehensively evaluating the two results. The present application captures the complex time series correlation and fusion features between power multi-modal data through a machine learning algorithm, realizes time series correlation analysis in multi-modal defect identification of power transmission line suspension insulator strings, and realizes multi-sensor data fusion and temperature compensation in overhead transmission conductor sag monitoring.

1. Name of the Design Product: On-line Monitoring System for Conductor Sag. 2. Use of the Design Product: Used for on-line monitoring system for conductor sag. 3. Design Key Points of the Design Product: Lie in the combination of shape and pattern. 4. Picture or Photograph that Best Illustrates the Design Key Points: Front View.

The invention discloses an inertial navigation parameter real-time estimation and updating method, system, equipment and medium for monitoring sag and windage yaw states of a power transmission line conductor, and belongs to the technical field of three-dimensional state monitoring of power transmission lines, and the inertial navigation parameter real-time estimation and updating method comprises the following steps: collecting inertial observation data of the power transmission line conductor; constructing an error state model, fusing the inertial observation data and the first auxiliary observation data by adopting a first filtering estimator, and performing real-time estimation of an error state; performing closed-loop feedback correction based on the error state; calculating sag parameters and windage yaw parameters of the transmission line conductor according to the navigation state; and performing time sequence analysis, and outputting a safety state monitoring result of the power transmission line conductor. By establishing the error state model, online estimation and real-time compensation of the navigation error and the zero offset of the sensor are realized, the sag and windage yaw parameters of the power transmission line conductor are calculated based on the corrected high-precision navigation, and the power transmission line conductor three-dimensional state real-time monitoring method suitable for the complex environment is formed.

The invention discloses a method and a device for predicting height change of an ultra-high voltage transmission conductor, and relates to the technical field of intelligent operation and maintenance of transmission lines. According to the main technical scheme, the method comprises the steps that operation state parameter data and static parameter data corresponding to a current wire are acquired; the operation state parameter data of the current conductor and the inherent parameter data of the line are processed by using the pre-constructed conductor height change prediction model so as to predict and output the actual conductor sag data of the current conductor, and the conductor height change prediction model is based on a mechanism model based on a physical principle, so that the prediction reliability is ensured, and the prediction accuracy is improved. Meanwhile, a data driving method is used for correcting and optimizing the model, the prediction precision is improved, advantage complementation is achieved, and therefore a high-precision conductor sag prediction result is obtained; and real-time height data corresponding to the current lead is determined in combination with the static geographic parameter data of the current lead, and the real-time height data can be but not limited to the height to the ground or the clearance height to a ground obstacle.

The invention discloses a method for analyzing the influence of a thick insulating rubber anti-icing coating on the temperature rise and sag of a lead, which comprises the following steps of: firstly, analyzing the heat balance of the lead after coating a rubber insulating material, and then, improving the sag of the lead after coating the rubber insulating material. According to the method, an innovative classification model is provided for an overhead conductor sag evolution mechanism, and a deformation mechanism is decoupled into an irreversible composite effect and a reversible composite effect. Optimized design of coating parameters is realized by establishing a coupling influence model of an insulating rubber coating on a conductor temperature field, weight distribution and sag and by joint solution of a thermodynamic equation and a mechanical catenary equation.