Formalisms

Abstract

Vector-dyadic forms of the kinematical and dynamical equations of a multibody system are given as Eqs.8.1.1–2 to 4. Representing vectors rⁱ, ωⁱ, vⁱ and matrices A ⁱ by any suitable set of coordinates and velocities

$${x_I} = [{x_{Ii}}]\;\;\;\;{x_{II}} = [{x_{IIi}}]\;\;\;\;i = 1, \ldots, 6N$$

((1))

those vector-dyadic equations go over into corresponding matrix equations whose general forms are

$${\dot x_I} = {\hat X_I}({x_I}){x_{II}}$$

((2))

$$J\;{\dot x_{II}} = Q + \Lambda $$

((3))

The specific forms of matrix X̂ _I in the kinematical equations, Eqs.2, and of matrices J, Q, and Λ in the dynamical equations, Eqs.3, depend on the choice of variables x _I and x _II .