EMCH 532: Intermediate Dynamics

Intermediate Dynamics for Engineers: This class is offered every year during the Spring Semester for Mechanical and Aerospace Engineering students by Prof. Banerjee.

Course Topics

Topic 1: Review of Vector Calculus

• Introduction to Index Notation
• Review of Calculus of Variation (ref. 502)
• Review of Newtonian and Lagrangian description of motion (ref. 502)
• Introduction to the Vector Description of Rotating Bodies in 3D

Topic 2: Kinematics of a Particle, in Cartesian and Curvilinear coordinate systems

• Curvilinear coordinate system: Covariant and Contravariant
• Polar and Spherical Coordinate System
• Motion of particles along a curve
• Velocity, Acceleration, Linear, Angular Momentum & Areal Velocity
• Potential and Kinetic Energy

Topic 3: Kinetics, Motion of a Rigid Body, in Generalized coordinate systems

• Force, Torque, Work, Energy (Potential & Kinetic Energies) and Conservation of Energy of three-dimensional (3D) bodies.
• Angular Velocity, Angular Acceleration, Angular Momentum, and Impulse
• Rotating systems in 3D, Conservation of Linear and Angular Momentum
• Orbital Dynamics
• Body Kinetics

Topic 4: Dynamics of System of Rigid Bodies

• Dynamical Relations for System of Rigid Bodies
• 3D-Connected rigid body dynamics
• Dynamics of Geometrical Rod structures with and without multiple joints (Robotics application)

Topic 5: Steady State Unique Motion

• Gyroscopic & Precessional motion