Rigid Body Dynamics

This course unit concerns the study of rigid body mechanics. It is the natural continuation of the course unit devoted to the kinematics and statics of rigid bodies in L1. In this course unit, we will place ourselves in a dynamic framework and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the tensor of external actions, studied in L1, as well as knowledge of the dynamic tensor. The latter can be calculated using the kinetic tensor, which involves the concept of moment of inertia for a rigid solid. The main applications studied in this course 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 we will discuss the kinetic energy theorem.

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

Kinematics of rigid solids. Concept of torque. Torque of external forces. Fundamental principle of statics. First-year mathematics course (algebra and analysis).

CC

1. Brief reminders of rigid body kinematics: concept of rotation, kinematic torque, composition of movements, rolling without slipping

II Brief reminders of the Fundamental Principle of Statics and applications

III Mass geometry

IV Kinetics: kinetic tensor, kinetic energy, dynamic tensor

1. Fundamental Principle of Dynamics: PFD, solid-solid interactions and friction laws, applications.
2. Kinetic energy theorem