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Direct Application Of The Least Action Principle To Solve (Human) Movement Dynamics Without Using Differential Equations Of Motion, Amitha Kumar
Theses
This thesis explores the numerical feasibility of solving motion 2-point boundary value problems (BVPs) by direct numerical minimization of the action without using the equations of motion (EOM) as an intermediate step. The proposed direct least action (DLA) approach using the downhill simplex method (DSM) is applied to both the single and double pendulum systems as beginning test problems. The solutions so obtained are compared to numerical solutions of the corresponding Lagrange BOM solved using a first order Euler algorithm for the same mechanical problems. The output path obtained by both of the methods essentially superimpose on each other.
Future …