Dynamics of the Rigid Solid

This unit concerns 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 will place ourselves in a dynamic framework and apply the Fundamental Principle of Dynamics. The writing of this principle requires the knowledge of the torsor of the external actions, studied in L1, but also the knowledge of the dynamic torsor. The latter can be calculated with the help of the kinetic torsor which, for a rigid solid, uses the notion of moment of inertia. The main applications studied in this unit concern the rigid solid or simple cases of articulated systems of rigid solids. In addition, we will study the particular case of contact and friction actions (Coulomb friction) and we will approach the Kinetic Energy Theorem.

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

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

CC

1. Brief reminder of kinematics of rigid solids: notion of rotation, kinematic torsor, composition of motions, rolling without sliding

II Brief reminder of the Fundamental Principle of Statics and applications

III Geometry of masses

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