Overview
Analytical Mechanics (a.k.a. Classical Mechanics ) is the study of how things move. It is the branch of physics that describes the behavior of macroscopic objects, ranging from pendulums to planetary orbits and galaxies. It is based on the fundamental principles (Newton’s Laws) laid down by Galileo and Newton in the 16th and 17th Centuries. It was then reformulated in the 19th Century by Euler, Lagrange, Hamilton and others to make it more powerful and elegant. While Classical Mechanics has been shown to be an incomplete theory that breaks down at the quantum level, at high velocities and in strong gravitational fields, it remains the most useful description of our everyday macroscopic world. Modern applications include areas in mechanical engineering, aerospace, chaos theory, celestial mechanics, molecular dynamics, fluid mechanics, computer animation and video game design.
Goals
At the end of the course students will be able to:
- Apply the concepts of forces, torques, momentum, angular momentum, energy and conservation laws to derive and solve mechanics problems.
- Construct, solve and apply the equations of motion for undamped, damped and forced oscillations.
- Solve mechanics problems using Lagrangian and Hamiltonian formalisms
- Solve the two-body central-force problem for a specified potential and apply the orbital equations.
- Solve and apply the equations of motion for objects in non-inertial reference frames.
- Calculate the moment of inertia tensor and solve for the principle moments and axes of a solid.
- Solve for the normal modes of a system of coupled oscillators.
- Use skills in computational thinking to solve mechanics problems.
Grades
Your grade for the course will be based on the following:
- 25% - Homework, Quizzes & Projects
- 40% - 2 exams @ 20% each
- 25% - Final cumulative exam
- 10% - Participation, Attendance and Discussion