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Mechanics
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T. Tsujioka
Advanced Seminar
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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 space

I. 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

 

 

 

 

 

 

 

 

 

 

 

 

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