Induced Symplectic Structures and Dynamics of a 2-Dimensional Space Robot

Abstract

We develop dynamics of a space robot which has a hyperregular Lagrangian in the context of Lagrangian systems. First, we show how the symplectic structure can be induced on the tangent bundle by using the Legendre transformation. Then, we formulate an intrinsic Lagrangian system with external forces and demonstrate an example of 2-dimensional space robots to derive equations of motion with conservations of linear and angular momentum.