Trajectory Generation between Two Arbitrary States Based on Hamilton's Principle a Variable Substitution Method

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 .