Title:

Author:

Mechanics

Copyright:

T. Tsujioka

Advanced Seminar

Mechanics

0. Mathematical Preliminaries

1. Vectors and coordinate systems

2. Differential Equations

2-1. Separation of variables

2-2. 2nd order Linear ODEs (Ordinary Differential Equations)

3. Kinematics

3-1. Coordinate System of observers, Coordinates of objects, Velocity and acceleration of linear motion

3-2. Angular velocity and acceleration of rotational motion in 2-D plane

3-3. General motion in 3-D spaceI. Newtonian Mechanics

4. Newton's laws

4-1. Linear momentum and Force; Newton's equation of motion

4-2. Conservation of linear momentum

4-3. Angular momentum and Torque

4-4. Conservation of angular momentum

5. Mechanical Energy

5-1. Work and power

5-2. Potential energy in conservative field

5-3. Kinetic energy of moving objects

5-4. Conservation of mechanical energy

6. Universal Gravitation

6-1. Newtonian mass and center of mass

6-2. Newton's law of universal gravitation

6-3. Planetary motion in gravitational potential well

7. Mechanical Oscillations

7-1. Simple oscillations

7-2. Forced and damped oscillations

II. Lagrangian Mechanics

8. Lagrangian and Hamiltonian

8-1. Variation principle and Euler's equation

8-2. Lagrange's equation of motion

8-3. Hamilton's equation of motion in phase space

8-4. Noether's theorem

9. System of Mass points

9-1. Motion of mass points

9-2. Normal modes of oscillations of mass points

10. Rigid-body Mechanics

10-1. Coordinate system in a rigid-body

10-2. Moment of inertia, Ellipsoid of inertia

10-3. Angular momentum of a rigid-body and Equation of motion of a rigid-body

10-4. Motion of a rigid-body in 2-D plane

10-5. Motion of a rigid-body in 3-D space