Goldstein Notes: Chapter 1 - Survey of Elementary Particles
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Course
PHY - 502
Institution
Savitribai Phule Pune University
Book
Classical Mechanics
This is self written transcription to the first chapter of Goldstein's Classical Mechanics, which covers an in depth and easy to understand translation of the physics involved and a more in depth approach to the mathematics which is skipped in the book for conciseness and brevity.
Calicut University,M. SC Physics, First Semester, Phy1c01, Classical Mechanics Kinematics of a rigid body
PHY2601 Assignment 2 (COMPLETE ANSWERS) 2024
PHY2601 Exam Portfolio October November 2023
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Goldstein Notes
by Dennil Joby
A complete transcription to ”Classical Mechanics” by Goldstein et.al.,
June 20, 2024
,Contents
1 Survey of Elementary Particles 2
1.1 Single Particle Mechanics . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Conservation Theorems . . . . . . . . . . . . . . . . . . . 3
1.1.2 Work and Energy of a Particle . . . . . . . . . . . . . . . 4
1.2 Mechanics of a System of Particles . . . . . . . . . . . . . . . . . 6
1.2.1 Linear and Angular Momentum of a System . . . . . . . . 6
1.2.2 Weak and Strong Law of Action and Reaction . . . . . . 8
1.2.3 Angular Momentum in terms of Center of Mass . . . . . . 8
1.2.4 Work and Energy . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 Types of Constraints . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Disk on a Surface . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 D’Alembert’s Principle . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 ⃗ri → ⃗qj Transformation Equations . . . . . . . . . . . . . 14
1.5 Application of the Lagrangian to Electromagnetic Systems . . . . 18
1.5.1 Expressing the force in terms of U (q, q̇) . . . . . . . . . . 19
1.5.2 Gaining the Lorentz Force from the Lagrangian . . . . . . 21
1.5.3 Dealing with ”extra” Forces . . . . . . . . . . . . . . . . . 22
1
, 1 Survey of Elementary Particles
1.1 Single Particle Mechanics
For a given coordinate system for a particle of mass m, its position be defined
by its position/radius vector ⃗r. Following this we define the particle’s velocity
and consequently the momentum respectively as;
d
⃗v = ⃗r (1)
dt
p⃗ = m⃗v (2)
while equation (1) and its derivatives together establish the kinematics of the
particle, equation (2) and especially its first derivative establish the dynamics
of the particle.
Essentially,
d
F⃗ = p⃗ (3)
dt
which is the crux of Newton’s second Law, which states that for a given frame
of reference the force exerted on a particle is proportional (equal to be precise)
to the rate of change of momentum of the particle.
In most cases we’ll see that a particle’s mass remains constant, which leads to
alternative forms of equation (3) such as,
d
F⃗ = m ⃗v
dt
d2 (4)
= m 2 ⃗r
dt
= m⃗a
Thus our equation of motion is a second order differential equation1 .
1 assuming ⃗ does not depend on higher order derivatives
F
2
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