Rigid Body Dynamics

This unit focuses on the mechanics of rigid bodies. It is the natural continuation of the unit on the kinematics and statics of rigid bodies covered in the first year of undergraduate studies. In this unit, we will adopt a dynamic framework and apply the Fundamental Principle of Dynamics. Deriving this principle requires knowledge of the torque of external forces, which was studied in the first year, as well as knowledge of the dynamic torque. The latter can be calculated using the kinetic torque, which, for a rigid body, involves the concept of moment of inertia. The main applications studied in this unit concern rigid bodies or simple cases of articulated systems of rigid bodies. In addition, we will study the special case of contact and friction forces (Coulomb friction) and discuss the Kinetic Energy Theorem.

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

Kinematics of rigid bodies. Concept of torsion. Torsion caused by external forces. Fundamental principle of statics. First-year mathematics courses (algebra and calculus).

CC

1. Brief review of the kinematics of rigid bodies: the concept of rotation, kinematic torque, composition of motions, and rolling without slipping

II Brief Review of the Fundamental Principle of Statics and Its Applications

III Geometry of Masses

IV Kinematics: Kinematic Torque, Kinetic Energy, Dynamic Torque

1. Fundamental Principle of Dynamics: FPD, Solid-Solid Interactions, and Laws of Friction; Applications.
2. Kinetic Energy Theorem