Syllabus

1. Review of Planar Kinematics  

2. Spatial Kinematics

Motion of a particle in terms of rectangular, cylindrical, and spherical components.

Motion of a particle as described by path-frame components and parameters.

Representation of vectors in different reference frames.

Transformation and rotation matrices. Direction cosine matrices. Euler angles.

Rotation of vectors.

Angular velocity and acceleration relationships.

Motion of a particle with respect to differently moving reference frames.

   3. Review of Newtonian Dynamics

Inertial and noninertial reference frames. Three laws of Newton.

Force-acceleration relationships.

Impulse-momentum relationships. Impulsive forces.

Work-energy relationships. Conservative and nonconservative forces. Potential energy.

    4. Newtonian Dynamics of Rigid Bodies

Inertia tensor and its matrix representation in different reference frames.

Newton-Euler equations.

Interacting rigid bodies.

Gyroscopes.

 5. Dynamics via Work and Energy Principles

Generalized coordinates and forces.

Virtual work principle.

Lagrange’s equations.

 Systems with constraints.