scholarly journals Natural Motion Trajectory Generation Based on Hamilton's Principle

2006 ◽  
Vol 42 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Susumu MORITA ◽  
Toshiyuki OHTSUKA
Keyword(s):  
Trajectory Generation ◽  
Motion Trajectory ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Natural Motion

TRAJECTORY GENERATION BETWEEN TWO ARBITRARY STATES BASED ON HAMILTON'S PRINCIPLE A VARIABLE SUBSTITUTION METHOD

2012 ◽  
Vol 09 (03) ◽  
pp. 1250023 ◽  
Author(s):  
SUSUMU MORITA
Keyword(s):  
Lagrange Equation ◽  
Trajectory Generation ◽  
Modern Science ◽  
Mathematical Explanation ◽  
Hamilton’S Principle ◽  
Human Beings ◽  
Motion Generation ◽  
Hamilton's Principle ◽  
Variable Substitution ◽  
Human Motions

Motion principles of animals and humans has been a field of interest for over half a century. As for human motions, the study by modern science started off by a Soviet physiologist in the 1930's, followed by many proposals of models and principles to explain how human beings move. This paper introduces an alternative motion principle with a motion generation method. The subject in discussion is the Hamilton's principle which yields equation of free motion. The motion generation method is derived based on a novel variable substitution to be applied to the Hamilton's principle which then yields the Euler–Lagrange equation that can be used for motion trajectory generation between two arbitrary states. A numerical example with measured data is shown, and a mathematical explanation of the variable substitution and the qualitative meaning of the trajectory generation method is given.

Dynamic Modeling of Satellite Tether Systems Using Newton’s Laws and Hamilton’s Principle

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Kalyan K. Mankala ◽  
Sunil K. Agrawal
Keyword(s):  
Dynamic Modeling ◽  
Continuous System ◽  
Variable Length ◽  
Variable Domain ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Newton’S Laws

The objective of this paper is to derive the dynamic equations of a tether as it is deployed or retrieved by a winch on a satellite orbiting around Earth using Newton’s laws and Hamilton’s principle and show the equivalence of the two methods. The main feature of this continuous system is the presence of a variable length domain with discontinuities. Discontinuity is present at the boundary of deployment because of the assumption that the stowed part of the cable is unstretched and the deployed part is not. Developing equations for this variable domain system with discontinuities, specially using Hamilton’s principle, is a nontrivial task and we believe that it has not been adequately addressed in the literature.

Dynamics of 3D Micropolar Gyroelastic Beams

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Modeling ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
The Finite Element Method ◽  
Hamilton's Principle ◽  
Modeling And Analysis ◽  
Element Method

This paper is devoted to the dynamic modeling of micropolar gyroelastic beams and explores some of the modeling and analysis issues related to them. The simplified micropolar beam torsion and bending theories are used to derive the governing dynamic equations of micropolar gyroelastic beams from Hamilton’s principle. Then these equations are solved numerically by utilizing the finite element method and are used to study the spectral and modal behaviour of micropolar gyroelastic beams.

Modified Hamilton's Principle

1973 ◽  
Vol 41 (10) ◽  
pp. 1188-1190 ◽  
Author(s):  
John R. Ray
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle
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