Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Center Of Mass ◽  
Solution Process ◽  
Body System ◽  
Efficient Treatment ◽  
Composite Body ◽  
Recursive Solution ◽  
System A ◽  
Principal Axes ◽  
Solution Methods ◽  
The Moment

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest include the reaction wheels in satellites, wheels on a car, and flywheels in machines. More specifically, these bodies have diagonal inertia tensors. They spin about one of its principal axes, with the moment of inertia along the transverse axes identical. Their center of mass lies on the spin axis. Current recursive solution methods treat these bodies identically as any other body in the system. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order(N−m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

2007 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Center Of Mass ◽  
Solution Process ◽  
Body System ◽  
Efficient Treatment ◽  
Composite Body ◽  
Recursive Solution ◽  
System A ◽  
Principal Axes ◽  
Solution Methods ◽  
Treat All

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest are the reaction wheels in satellites, wheels on a car, propellers on a helicopter and flywheels in machines. Each such body spins about one of its principal axes and around its center of mass. Current recursive solution methods treat all bodies in the system identically. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order O(N-m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

Zur exakten Behandlung von kollektiven Rotational Teil B: Anwendungen / On the Exact Treatment of Collective Rotations. Part B: Applications

1973 ◽  
Vol 28 (9) ◽  
pp. 1500-1515
Author(s):  
Hanns Ruder
Keyword(s):  
Exact Expression ◽  
Quantum Mechanical ◽  
Body System ◽  
Identical Particles ◽  
Moments Of Inertia ◽  
Fixed Frame ◽  
Principal Axes ◽  
The Moment ◽  
Quantum Mechanical Systems ◽  
Body Fixed Coordinate System

In part B we deal with some applications and conclusions of the theory for collective rotations of quantum mechanical systems which has been treated in part A. In the first section we investigate the consequences of a body-fixed coordinate-system lying in the principal axes of inertia. We find that for this choice in general no specific decoupling is obtained, and therefore the so-called hydrodynamic moments of inertia are always a lower limit for the real moments of inertia of a system. Further the transition from a n-body system to the rigid body is carried out. In another section the symmetry conditions of systems with identical particles are treated. Especially we study the question how to define the optimal body-fixed frame of reference in a system of independent identical particles. Finally we compare the results of our exact theory of collective rotations with the results of the cranking model and find that only in the limit of an infinitely heavy core the cranking model leads to an exact expression for the moment of inertia.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

MULTISTAGE ROCKET FLIGHT SIMULATION

2019 ◽  
pp. 105-107
Author(s):  
A. S. Busygin ◽  
А. V. Shumov
Keyword(s):  
State Vector ◽  
Center Of Mass ◽  
Flight Simulation ◽  
Continuous Change ◽  
Information Tools ◽  
The Earth ◽  
Proposed Model ◽  
Piecewise Continuous ◽  
The Moment ◽  
Simulated Object

The paper considers a method for simulating the flight of a multistage rocket in Matlab using Simulink software for control and guidance. The model takes into account the anisotropy of the gravity of the Earth, changes in the pressure and density of the atmosphere, piecewise continuous change of the center of mass and the moment of inertia of the rocket during the flight. Also, the proposed model allows you to work out various targeting options using both onboard and ground‑based information tools, to load information from the ground‑based radar, with imitation of «non‑ideality» of incoming target designations as a result of changes in the accuracy of determining coordinates and speeds, as well as signal fluctuations. It is stipulated that the design is variable not only by the number of steps, but also by their types. The calculations are implemented in a matrix form, which allows parallel operations in each step of processing a multidimensional state vector of the simulated object.

Motion Simulation of Key Components in a Package Machine

2012 ◽  
Vol 557-559 ◽  
pp. 2303-2306
Author(s):  
Shu Bin Kan
Keyword(s):  
Structural Parameters ◽  
Center Of Mass ◽  
Motion Simulation ◽  
Software Environment ◽  
Optimization Result ◽  
Adams Software ◽  
Motion Characteristic ◽  
The Moment ◽  
Selection Of

The motion characteristic of key components is a decisional factor to the working reliability and stability of a package machine. In this paper, the motion simulation of a key component is carried out in the ADAMS software environment. By analysis of the force, variance of the center-of-mass and the moment of the component, the mutation point in the motion is found, and then the structure is optimized by selection of different structural parameters. The optimization result shows a significant improvement for the reliability and stability of the whole machine.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

Finding Principal Axes of Complex Plane Rigid Body with Rending-Image of MATLAB

2012 ◽  
Vol 490-495 ◽  
pp. 2156-2159
Author(s):  
Wu Gang Li
Keyword(s):  
Rigid Body ◽  
Complex Plane ◽  
Principal Axis ◽  
Flat Surface ◽  
Moment Of Inertia ◽  
Principal Axes ◽  
The Moment

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical

Balance Recovery based on Whole-Body Control using Joint Torque Feedback for Quadrupedal Robots

2021 ◽  
pp. 1-18
Author(s):  
Young Hun Lee ◽  
Hyunyong Lee ◽  
Hansol Kang ◽  
Jun Hyuk Lee ◽  
Ji Man Park ◽  
...  
Keyword(s):  
Force Feedback ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Joint Torque ◽  
Whole Body ◽  
External Disturbances ◽  
Feed Forward ◽  
The Moment ◽  
Joint Torque Feedback ◽  
Capture Point

Abstract In legged locomotion, the contact force between a robot and the ground plays a crucial role in balancing the robot. However, in quadrupedal robots, general whole-body controllers generate feed-forward force commands without considering the actual torque or force feedback. This paper presents a whole-body controller by using the actual joint torque measured from a torque sensor, which enables the quadrupedal robot to demonstrate both dynamic locomotion and reaction to external disturbances. We compute external joint torque using the measured joint torque and the robot's dynamics, and then transform this to the moment of the center of mass (CoM). Using the computed CoM moment, the moment-based impedance controller distributes a feed-forward force corresponding to the desired moment of the CoM to stabilize the robot's balance. Furthermore, to recover balance, the CoM motion is generated using capture point-based stepping control and zero moment point trajectory. The proposed whole-body controller was tested on a quadrupedal robot, named AiDIN-VI. Locomotive abilities on uneven terrains and slopes and in the presence of external disturbances are verified through experiments.

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