Goldstein Notes: Chapter 1 - Survey of Elementary Particles
7 views 0 purchase
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
All for this textbook (4)
Written for
Savitribai Phule Pune University
PHY - 502
All documents for this subject (1)
Seller
Follow
denniljoby
Content preview
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller denniljoby. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R214,32. You're not tied to anything after your purchase.
