This course aims to train the students in the following topics of kinematics and dynamics of spatial systems.

1. Particle kinematics: Rectangular, cylindrical, and spherical coordinates.

2. Path frame description of motion: Tangential and normal accelerations. Center and radius of curvature. Torsion. Curve-tracking and torsional angular velocities.

3. Vectors and Dyadics. Rotation of a vector and rotation dyadic.

4. Matrix representation of vectors and dyadics in different reference frames. Component transformation matrices.

5. Vector differentiation with respect to different reference frames. Coriolis-Transport theorem. Relative angular velocities and accelerations.

6. Velocity and acceleration of a point with respect to different reference frames.

7. Newtonian mechanics for a particle: Three laws of Newton. Force-acceleration, impulse-momentum, and work-energy relationships.

8. Newtonian mechanics for a system of particles: Force-acceleration, impulse-momentum, and work-energy relationships.

9. Conservative forces and potential energy.

10. Newtonian mechanics for a rigid body.

11. Newtonian mechanics for a system of rigid bodies. Interaction forces and moments.

12. Dynamic analysis via work-energy methods. Virtual work method based on d'Alembert's principle. Hamilton's principle.

13. Lagrange's equations without constraints.

14. Lagrange's equations with holonomic and nonholonomic constraints. Lagrange multipliers and constraint forces.