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PHY301Sciences3 Unitsintermediate

Classical Mechanics II

This course introduces fundamental principles of classical mechanics. It covers constraints, generalized coordinates, motion under central conservative forces, and scattering. Students will explore Kepler's laws, motion in non-inertia frames, and Lagrange's and Hamilton's formulations. The course aims to equip learners with analytical skills applicable in various fields of physics and engineering, emphasizing problem-solving and theoretical understanding of mechanical systems.

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156h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
Classical MechanicsLagrangian MechanicsHamiltonian MechanicsCentral ForcesConstraints

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Constraints

2

Generalized Coordinates

3

Lagrangian Mechanics

4

Hamiltonian Mechanics

5

Central Force Motion

6

Kepler's Laws

7

Scattering Cross Sections

8

Non-Inertial Frames

Total Topics8 topics

Requirements

Knowledge and skills recommended for success

PHY 201: Analytical Mechanics

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assessments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Theoretical Physicist

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Research Scientist

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Aerospace Engineer

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Mechanical Engineer

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Data Analyst

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Industry Applications

Real-world sectors where you can apply your knowledge

AerospaceDefenseResearch and DevelopmentAcademiaEngineering

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Generalized Coordinates and Constraints

4h

Unit 1: Constraints

2 study hours
  • •Define degrees of freedom and constraints.
  • •Distinguish between holonomic and non-holonomic constraints.
  • •Give examples of holonomic and non-holonomic constraints.

Unit 2: Generalized Coordinates

2 study hours
  • •Write physical quantities in terms of generalized coordinates.
  • •Use constraints equation to define different generalized coordinate schemes.
  • •Calculate azimuthal angle.
Week
2

Module 1: Generalized Coordinates and Constraints

3h

Unit 3: Virtual work, Virtual Displacement and Generalized Forces

3 study hours
  • •Explain virtual displacement, virtual work and generalized forces.
  • •Express total differential of any set of system position vectors in terms of virtual displacement.
  • •Solve related problems.
Week
3

Module 2: Lagrange's and Hamilton's formulation of mechanics

3h

Unit 1: D'Alembert's Principle of Virtual Work

3 study hours
  • •Derive D'Alembert's Principle from Newton's Second Law Of Motion.
  • •Reformulate Newton's equations system as a system of equations for the generalized coordinates.
  • •Use D'Alembert's principle to relate generalized forces to the rate of change of the momenta.
Week
4

Module 2: Lagrange's and Hamilton's formulation of mechanics

3h

Unit 2: Lagrangian Mechanics

3 study hours
  • •Express the Lagrangian L in Cartesian coordinates.
  • •Transform L to generalized coordinates.
  • •Give Lagrange's equations in generalized coordinates.
Week
5

Module 2: Lagrange's and Hamilton's formulation of mechanics

3h

Unit 3: Hamiltonian Mechanics

3 study hours
  • •Explain Legendre transform.
  • •Understand the application of legendre transform in thermodynamics.
  • •Find the Legendre transform of any function.
Week
6

Module 3: Central force and scattering

3h

Unit 1: The Generic Central Force Problem

3 study hours
  • •Define central force and know the properties of an isolated two body central force system.
  • •Discuss the reduction of the two body problem to a mathematically equivalent problem of a single particle moving in one direction.
  • •Explain different shape of the effective potential energy function and its implications for the motion of the system.
Week
7

Module 3: Central force and scattering

3h

Unit 2: Kepler's Problem

3 study hours
  • •State the three Kepler's Laws.
  • •Prove the three Keplers laws.
  • •Define an orbit.
  • •Derive and explain the conic equation of an orbit.
Week
8

Module 3: Central force and scattering

3h

Unit 3: Scattering Cross Section

3 study hours
  • •State the expression for energy of a system of particle incident on a force center subject to a scattering potential.
  • •Calculate the differential cross section.
  • •Calculate the total cross section.
Week
9

Module 4: Motion in non-inertia reference frame

3h

Unit 1: Time Derivative in Fixed and Rotating Frames

3 study hours
  • •Derive the time derivatives of vector A in fixed and rotating reference frame.
  • •State the expressions for translational velocity and acceleration, V and A respectively.
  • •Determine the relationship between the velocities of fixed and rotating reference frame.
Week
10

Module 4: Motion in non-inertia reference frame

3h

Unit 2: Motion Relative to Earth

3 study hours
  • •Represent the rotation of the earth in terms of fixed frame of latitude angle λ and the azimuthal angle ψ.
  • •State the expression for acceleration of a point as observed in the rotating frame O.
  • •State the expression for pure gravitational acceleration in the rotating frame of the Earth.
Week
11

Final Revision

4h

Final Revision

4 study hours
  • •Review all modules
  • •Work on assignments
  • •Prepare for TMAs
Week
12

Final Revision

4h

Final Revision

4 study hours
  • •Complete any outstanding assignments
  • •Review difficult concepts
  • •Practice problem-solving
Week
13

Final Revision

4h

Final Revision

4 study hours
  • •Focus on key concepts
  • •Review formulas and equations
  • •Simulate exam conditions

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Prioritize understanding of core concepts: Lagrangian and Hamiltonian mechanics, central forces, and non-inertial frames.

2

Practice solving a variety of problems from each unit, focusing on applying theoretical knowledge to practical scenarios.

3

Create concept maps linking different modules to reinforce connections between topics.

4

Review all Tutor-Marked Assignments (TMAs) and address any feedback from your tutor.

5

Allocate specific time slots for revision each week, focusing on areas of weakness.

6

Practice past exam papers under timed conditions to improve speed and accuracy.

7

Formulate a study group to discuss challenging concepts and share problem-solving strategies.

8

Focus on understanding the derivations of key equations, not just memorizing them.

9

Create flashcards for important formulas and definitions to aid memorization.

10

Ensure you understand the applications of each concept to real-world scenarios.

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