Date of Award
Master of Science in Biomedical Engineering - (M.S.)
H. Michael Lacker
Richard A. Foulds
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 steps will be to apply DLA to more complicated multi-branched pendulum systems that are used to model the human body and to apply more efficient numerical methods than the DSM algorithm to DLA. Eventually if numerical algorithms can be developed that make the DLA approach as efficient or more efficient than using Lagrange's differential EOM to solve 2-point BVPs for multi-branched pendulum systems then such algorithms will be embedded in the software that we have developed and use in the human motion analysis and performance laboratory at NJIT to solve for human motion problems. The software employs a new method called the Boundary Method® a new mathematical technique developed in our laboratory. This method solves simultaneously for both new motions that can accomplish a given motor task and the net muscular joint forces required to produce those new motions.
Kumar, Amitha, "Direct application of the least action principle to solve (human) movement dynamics without using differential equations of motion" (2006). Theses. 427.