On the GAUSS Principle in the Numerical Integration of Mechanical Systems

Abstract

Here we consider mechanical systems with their configuration described by the in general non-minimal coordinates q₁,q₂,…,q_n which we arrange in a column matrix as q := (q₁,q₂,…,q_n)^T The system is subjected to constraints of the form

$${{c}_{i}}(q,\dot{q},t) = 0,i = 1,2, \ldots ,m$$

((1))

which we also write as

$$c(q,\dot{q},t): = {{({{c}_{1}},{{c}_{2}}, \ldots {{c}_{m}})}^{T}} = 0$$

((2))