Classical Mechanics II
- Sciences
- 300 level
- 3 credit units
- 136 pages
- 11 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 156 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- PHY 201: Analytical Mechanics
- Assignments
- Tutor Marked Assessments
- Final Examination
What you'll read
The real module and unit structure of PHY301, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
PHY301 · UNIT 1 CONSTRAINTS
The number of degrees of freedom is defined as the number of independent coordinates that is needed to identify uniquely the configuration of the system.
What you should be able to do
- Explain and distinguish between different classes of constraints.
- Express physical quantities in terms of generalized coordinates.
- Calculate the Lagrangian and Lagrange's equation of motion for physical systems.
- Calculate the Hamiltonian and Hamilton's equation of motion for physical systems.
- Describe motion under central conservative force.
- Explain scattering cross section.
- Determine the time derivatives of motion in fixed and rotating reference frames.
- Explain the motion relative to earth and its application in a free falling object.
What it prepares you for
- Theoretical Physicist
- Research Scientist
- Aerospace Engineer
- Mechanical Engineer
- Data Analyst
- Aerospace
- Defense
- Research and Development
- Academia
- Engineering
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 2: Lagrange's and Hamilton's formulation of mechanics
Unit 3: Hamiltonian Mechanics
The Legendre transform requires a strong understanding of multivariable calculus and its application to physical systems, which can be challenging for students without a solid mathematical background.
- Module 3: Central force and scattering
Unit 3: Scattering Cross Section
The mathematical derivations and conceptual understanding of differential and total cross-sections require a strong foundation in calculus and physics.
A suggested way through it
13 weeks, about 43 hours in total. Yours will differ.
- Week 1Module 1: Generalized Coordinates and Constraints
Unit 1: Constraints · 2 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 hours
Write physical quantities in terms of generalized coordinates.. Use constraints equation to define different generalized coordinate schemes.. Calculate azimuthal angle..
- Week 2Module 1: Generalized Coordinates and Constraints
Unit 3: Virtual work, Virtual Displacement and Generalized Forces · 3 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 3Module 2: Lagrange's and Hamilton's formulation of mechanics
Unit 1: D'Alembert's Principle of Virtual Work · 3 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 4Module 2: Lagrange's and Hamilton's formulation of mechanics
Unit 2: Lagrangian Mechanics · 3 hours
Express the Lagrangian L in Cartesian coordinates.. Transform L to generalized coordinates.. Give Lagrange's equations in generalized coordinates..
- Week 5Module 2: Lagrange's and Hamilton's formulation of mechanics
Unit 3: Hamiltonian Mechanics · 3 hours
Explain Legendre transform.. Understand the application of legendre transform in thermodynamics.. Find the Legendre transform of any function..
- Week 6Module 3: Central force and scattering
Unit 1: The Generic Central Force Problem · 3 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 7Module 3: Central force and scattering
Unit 2: Kepler's Problem · 3 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 8Module 3: Central force and scattering
Unit 3: Scattering Cross Section · 3 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 9Module 4: Motion in non-inertia reference frame
Unit 1: Time Derivative in Fixed and Rotating Frames · 3 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 10Module 4: Motion in non-inertia reference frame
Unit 2: Motion Relative to Earth · 3 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 11Final Revision
Final Revision · 4 hours
Review all modules. Work on assignments. Prepare for TMAs.
- Week 12Final Revision
Final Revision · 4 hours
Complete any outstanding assignments. Review difficult concepts. Practice problem-solving.
- Week 13Final Revision
Final Revision · 4 hours
Focus on key concepts. Review formulas and equations. Simulate exam conditions.
Preparing for the exam
- Prioritize understanding of core concepts: Lagrangian and Hamiltonian mechanics, central forces, and non-inertial frames.
- Practice solving a variety of problems from each unit, focusing on applying theoretical knowledge to practical scenarios.
- Create concept maps linking different modules to reinforce connections between topics.
- Review all Tutor-Marked Assignments (TMAs) and address any feedback from your tutor.
- Allocate specific time slots for revision each week, focusing on areas of weakness.
- Practice past exam papers under timed conditions to improve speed and accuracy.
- Formulate a study group to discuss challenging concepts and share problem-solving strategies.
- Focus on understanding the derivations of key equations, not just memorizing them.
- Create flashcards for important formulas and definitions to aid memorization.
- Ensure you understand the applications of each concept to real-world scenarios.
Questions students ask about this course
What is PHY301 about?
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.
How many units does PHY301 have?
PHY301, Classical Mechanics II, has 11 units across 4 modules, over 136 pages of course material. You can read it one unit at a time.
How many credit units is PHY301?
PHY301 carries 3 credit units, at 300 level in Sciences.
Is PHY301 hard?
PHY301 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does PHY301 take to study?
About 156 hours of study, spread across its 11 units.
How is PHY301 assessed?
PHY301 is assessed by Assignments, Tutor Marked Assessments and Final Examination.
What do I need before starting PHY301?
PHY 201: Analytical Mechanics
What can I do with PHY301?
Theoretical Physicist, Research Scientist, Aerospace Engineer, Mechanical Engineer and Data Analyst.