Intrinsic Modeling of Mechanical Systems Based on Geometry

The goal of this contribution is to show how differential geometric concepts appear in the context with mechanics. It will be pointed out how bundles and connections can be used to describe the concept of a space-time and to derive the velocity and the acceleration of a mass point in an intrinsic manner compatible with bundle morphisms that involve time explicitly. Furthermore the equations of motion will be derived using a covariant derivative which is constructed out of a special dynamic connection which is an extension of the well known Levi-Civita connection of classical mechanics. We will extend this intrinsic concepts to the case of a continuum and furthermore we will show how the partial differential equations that appear can be reduced to describe a rigid body motion.