Rigid Solid Dynamics

This unit deals with the study of the mechanics of rigid solids. It is the natural continuation of the unit devoted to the kinematics and statics of rigid solids in L1. In this unit, we'll take a dynamic approach and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the external action torsor, studied in L1, as well as knowledge of the dynamic torsor. The latter can be calculated using the kinetic torsor, which for a rigid solid involves the notion of moment of inertia. The main applications studied in this unit concern rigid solids or simple cases of articulated systems of rigid solids. In addition, we will study the special case of contact and friction actions (Coulomb friction) and the Kinetic Energy Theorem.

a. Isolate a mechanical system and assess the applied forces
b. Parameterize (model) a system, apply PFDs
c. Determine motion when forces are known
d. Determine linkage forces when motion is known
e. Linearize equations of motion around an equilibrium 

Kinematics of rigid solids. Notion of torsor. Torsor of external forces. Fundamental principle of statics. L1 mathematics course (algebra and analysis).

CC

1. Brief reminder of the kinematics of rigid solids: notion of rotation, kinematic torsor, composition of motions, non-slip rolling

II A brief review of the Fundamental Principle of Statics and its applications

III Mass geometry

IV Kinetics: kinetic torsor, kinetic energy, dynamic torsor

1. Fundamental principle of dynamics: PFD, solid-solid actions and friction laws, applications.
2. Kinetic energy theorem