Abstract
The Lie group of virtual displacement operators in Rodrigues-Hamilton parameters is constructed and equations of motion are derived for a heavy rigid body with one fixed point. It is shown that the addition (subtraction) of a term of the form df dt , f( t, x) ϵ C 2, to (from) the generalized Lagrangian L ∗(t,x,η) does not affect the form of the Poincaré and Chetayev equations. These equations can also be used to describe the relative motion of a holonomic system relative to a moving system of coordinates. Hamel's equations in non-linear quasi-coordinates are derived without using the transitivity equations, are compared with the generalized Poincaré equations and are transformed to Chetayev canonical form.
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