The discrete adjoint method in multibody dynamics

Abstract eng:
A problem arising frequently in multibody dynamics is to determine unknown input signals such that an objective function is minimized. The adjoint method is the most efficient way to compute the gradient of any objective function by solving a system of ”adjoint” differential algebraic equations backwards in time. The key idea of this method can also be applied directly to the time-discrete multibody system resulting in a set of adjoint difference equations, which yield the gradient of the discretized objective function. In this paper we present the discrete adjoint equations associated to the equations of motion of a multibody system, which are discretized by any implicit one-step integration method and describe how the obtained gradients can be transformed for varying time discretizations.

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