An improved constraint stabilisation technique for Udwadia-Kalaba Formulation

Abstract

This work seeks to further refine the current techniques required in constraining the solutions of a dynamical system onto the defined algebraic constraints by means of projection and constraint stabilization. The mechanical problems concerned in this work are expressed in the form of differential algebraic equations (DAE) consisting of a system of ordinary differential equations (ODE) in addition to a set of algebraic equations which represents the constraint manifolds the solutions have to comply to. As a novelty of the
work, the kinematic constraints are reformulated such that they represents manifolds in the phase space, and the solutions of the kinematic ODE at each time step are projected onto the phase space manifolds. The new constraint stabilization formulation corresponding to the phase space is developed, and a variety of numerical simulations of different constraint types are conducted in order to compare the capabilities of the new formulation in conforming the solutions to constraint manifolds and preserving solution accuracy under different constraint conditions.

Date of Award	3 Oct 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Mark H Lowenberg (Supervisor) & Simon A Neild (Supervisor)