A modified HHT method for the numerical simulation of rigid body rotations with Euler parameters

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

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NUMERICAL SIMULATION OF BORE-INDUCED DYNAMIC BEHAVIOR OF RIGID BODY USING 2-D MULTIPHASE FLOW NUMERICAL MODEL

Coastal Structures 2007 ◽

10.1142/9789814282024_0130 ◽

2009 ◽

Cited By ~ 1

Author(s):

Koji Kawasaki ◽

Norimi Mizutani

Keyword(s):

Numerical Simulation ◽

Numerical Model ◽

Multiphase Flow ◽

Rigid Body ◽

Dynamic Behavior

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Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1649977 ◽

2004 ◽

Vol 126 (1) ◽

pp. 124-130 ◽

Cited By ~ 24

Author(s):

Ravishankar Shivarama ◽

Eric P. Fahrenthold

Keyword(s):

Rigid Body ◽

Three Dimensional ◽

Nonlinear Problems ◽

Potential Energy Function ◽

Rigid Body Dynamics ◽

Dynamics Modeling ◽

Euler Parameters ◽

Strongly Nonlinear ◽

Body Dynamics ◽

General Potential

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

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Numerical simulation of a moving rigid body in a rarefied gas

Journal of Computational Physics ◽

10.1016/j.jcp.2015.03.030 ◽

2015 ◽

Vol 292 ◽

pp. 239-252 ◽

Cited By ~ 10

Author(s):

Samir Shrestha ◽

Sudarshan Tiwari ◽

Axel Klar ◽

Steffen Hardt

Keyword(s):

Numerical Simulation ◽

Rigid Body ◽

Rarefied Gas

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Euler’s Equations of Rigid Body: Its Control and Synchronization using Active Control and Recursive Backstepping methods.

JOURNAL OF RESEARCH AND REVIEW IN SCIENCE ◽

10.36108/jrrslasu/8102/50(0112) ◽

2018 ◽

Vol 5 (1) ◽

Author(s):

Cornelius Ogab ◽

Babatunde Idowu ◽

Abiola Ogungbe ◽

Eugene Onori ◽

Olufunmilayo Ometan ◽

...

Keyword(s):

Numerical Simulation ◽

Steady State ◽

Rigid Body ◽

Active Control ◽

Lyapunov Stability ◽

Stability Theory ◽

Lyapunov Stability Theory ◽

Control Laws ◽

Control And Synchronization ◽

Methods Numerical

We present Euler’s Equation of Rigid Body, its control and synchronization using active control and recursive backstepping methods. Based on Lyapunov stability theory, control laws are derived to synchronize the chaotic system and also to control to a steady state as well as track to a desired function via recursive backstepping methods. Numerical simulation are shown to verify the results.

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