What is Classical Mechanics?
Throughout this course, you will learn the motion of particles and rigid bodies.
Traditionally, the title of this course is Classical Mechanics. However, this
course is more than just Mechanics.
Classical means the theory is n
Motion in a Noninertial Reference Frame
We usually choose an inertial reference frame to describe dynamic process. However, there are types of problems for which noninertial frame is more natural, such
as the motion of objects on the surface of the rotati
Hamiltons Principle Lagrangian and
Hamiltonian Dynamics
The equation of motion can be fully described by writing F = ma for each object
involved. Then, why do we need this chapter?
1. For some motion, Cartesian coordinate system may not be the best choice
Dynamics of a System of Particles
Thus far, we have treated our dynamical problems
primarily in terms of single particles. Here we extend
our discussion to describe the system of n particles.
After developing a general formalism, we spend most
time in des
CentralForce Motion
The central-force problem is one of the oldest physics problem since the development of quantitative formulation of mechanics.
1. The force between celestial bodies are governed by the universal law of gravitation which is central forc
Hamiltons Principle Lagrangian and Ha
miltonian Dynamics
The equation of motion can be fully described by writing F = ma for each object
involved. Then, why do we need this chapter?
1. For some motion, Cartesian coordinate system may not be the best choic
CentralForce Motion
The central-force problem is one of the oldest physics problem since the
development of quantitative formulation of mechanics.
1. The force between celestial bodies are governed by the universal law of
gravitation which is central forc
Oscillations
Assume the potential is only a function of position. When there is a stable equilibrium, the energy around the equilibrium position, x0, can be approximated by a
harmonic potential.
1 d 2V
V ( x) V ( x0 )
2 dx 2
x x0
x x0
2
1 d 3V
3! dx3
Dynamics of a System of Particles
Thus far, we have treated our dynamical problems
primarily in terms of single particles. Here we extend
our discussion to describe the system of n particles.
After developing a general formalism, we spend most
time in des
Special Notes on Functional Derivative
What is a function?
y( x) x 2 4 x 5
For a given input x, the output y is determined. This y is a function of x.
Numbers are the input of a function, and the output are also numbers.
A function maps a number (or sever
Coupled Oscillations
If more than one oscillators present, the oscillations are coupled, and their behaviors at a glance may look quite different from the one oscillator behavior.
In this chapter, we will learn that the motion of any oscillatory system ca