  In this paper, we present an efficient form of Volterra's equations of motion
for both unconstrained and constrained multibody dynamical systems that include
ignorable coordinates. The proposed method is applicable for systems with both
holonomic and nonholonomic constraints. Firstly, based on the definition of
ignorable coordinates, one of the motion constants (the generalized momentum
vector corresponding to the ignorable coordinates) is dealt with as a
constraint, which will be referred to as dynamical constraints. These
constraints, along with ordinary constraints, namely kinematical constraints,
are then used in the proposed method to derive motion equations. This approach
gives the minimum number of equations needed to study the behavior of a
dynamical system. Three simulation examples are provided to evaluate the
proposed method and to compare it to existing methods. The first case study is
a constrained dynamical system, which moves in two-dimensional space. The
second one is an unconstrained multibody system including three connected rigid
bodies. Finally, the last case study includes a cubic satellite that uses a
deployable boom to move a mass to a desired location. The results of the
numerical simulations are compared to the conventional methods and the better
performance of the proposed method is demonstrated.
