A Lagrangian Quasicoordinate Formulation for Dynamic Simulations of Multibody Systems

Utilizing the work of Quinn (1990), a new extension of Lagrange’s equation in terms of quasicoordinates is presented. “Global” forms of velocity and kinetic energy have been used in conjunction with identities introduced by Quinn, allowing a single equation, in a form similar to Newton’s 2nd law, to represent the entire set of rotational equations of motion for a system. This method may be used if the energies are explicit functions of angular velocities and coordinate transformation matrices. A new identity is introduced which represents the elimination of Coriolis terms for the entire system. The formulation is applicable to a large class of problems in the dynamics of structures, including spacecraft, robots, ground vehicles and aircraft. This formulation has been used in the simulation of a nontrivial problem. Roboticists and biologists, working with biologically inspired robotics, are interested in the exceptional locomotion capabilities of the cockroach. A 36 degree of freedom model is used to represent the movement of the cockroach, Blaberus discoidalis. Six 5 degree of freedom legs support a freely translating and rotating body. The model is driven by joint angles obtained by processing high speed video of the cockroach’s locomotion, and mass and length parameters are taken directly from the roach. Results have been consistent with those obtained previously by other researchers.