Application of graph theory to the determination of kinetic energy of rigid body systems
This paper extends the studies of \textit{J. Wittenburg} on: (*) ``Dynamics of systems of rigid bodies'' (1977; Zbl 0363.70004) using the graph theory. An important problem in the dynamic analysis of mechanical systems is the determination of the Lagrangian and specially of the kinetic energy. The author presents a new method for the calculation of the kinetic energy for a system of N rigid bodies having a tree structure (*), by mean of the graph theory. Expression of the kinetic energy is obtained in terms of the translational velocities \(\vec u_ i\) and rotational velocities \({\vec \omega}_ i\) \((i=1,...,N)\) of the solids. This expression contains essential system data (i.e. inertia characteristics and locations of certain points within the system) and the topological informations by means of the path matrix \(P^{(1)}\). This approach offers a systematic expression which can be used for many different systems. Detailed calculations are performed in the case of planar motion.
scientific article; zbMATH DE number 4049175