Abstract :
[en] A direct differentiation method and an adjoint variable method are proposed for
the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated
in a matrix Lie group framework. These methods rely on the linearization of the equations
of motion and/or of the time integration procedure. The simpler structure of the equations
of motion in the Lie group formalism appears as an advantage for that purpose. Lie bracket
contributions and the non-linearity of the exponential map need to be taken into account
in the sensitivity algorithms. Nevertheless, essential characteristics of formulations of the
direct differentiation method and the adjoint variable method on linear spaces are recovered.
Some implementation issues are discussed and two relevant examples illustrate the
properties of these methods.
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