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MTH315Sciences3 Unitsintermediate

Analytical Dynamics I

This course, Analytical Dynamics, is designed to teach students how mathematics can be applied to solve problems in contemporary science, technology, and engineering. It covers the basics of analytical dynamics, exposing students to the skills needed to achieve proficiency in this area of applied mathematics. The course explores concepts such as constraints, Lagrange's equations, simple harmonic motion, and Hamiltonian theory, preparing students for advanced studies and practical applications in various fields.

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208h
Study Time
13
Weeks
16h
Per Week
advanced
Math Level
Course Keywords
Analytical DynamicsLagrange EquationsHamiltonianConstraintsHarmonic Motion

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

Degree of Freedom

2

Constraints

3

Lagrange's Equation

4

Impulsive Motion

5

Simple Harmonic Motion

6

Newton's Laws of Motion

7

Work, Power, and Energy

8

Hamiltonian Theory

9

Calculus of Variation

10

Rectilinear Motion

11

Collision of Smooth Spheres

12

Moment of a Force

Total Topics12 topics

Requirements

Knowledge and skills recommended for success

MTH211: Calculus

PHY202: Classical 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 assignments

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

Mechanical Engineer

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Aerospace Engineer

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Robotics Engineer

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Physics Researcher

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Applied Mathematician

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Industry Applications

Real-world sectors where you can apply your knowledge

AerospaceRoboticsAutomotiveManufacturingResearch and Development

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1:

4h

Unit 1: Degree of Freedom

2 study hours
  • •Define degree of freedom and relate it to discrete and continuous systems.
  • •Calculate the total kinetic energy of a system of particles.
  • •Apply the conservation theorem for linear momentum to solve problems.

Unit 2: Constraints

2 study hours
  • •Define constraints and differentiate between holonomic and non-holonomic constraints.
  • •Explain D'Alambert's principle and its applications.
  • •Solve problems involving virtual work and virtual displacement.
Week
2

Module 2:

4h

Unit 1: Lagrange's Equation

4 study hours
  • •Apply Lagrange's equations to solve dynamical problems.
  • •Determine the Lagrange function for particles moving in a conservative force field.
  • •Derive Lagrange's equations for holonomic constraints.
Week
3

Module 3:

4h

Unit 1: Impulsive Motion

4 study hours
  • •Define impulsive motion and identify equations of motion for impulsive forces.
  • •Explain the concept of a conservative force field.
  • •Solve problems involving the impact of two forces.
Week
4

Module 4:

4h

Unit 1: Simple Harmonic Motion

2 study hours
  • •Define simple harmonic motion (SHM) and identify the forces causing it.
  • •Explain the suspension of a particle by an elastic string.
  • •Define conical pendulum and solve related problems.

Unit 2: Collation of Smooth Spheres

2 study hours
  • •Define and explain the collision of smooth spheres.
  • •Apply the laws for the impact of spheres in direct and indirect impacts.
  • •Solve problems involving the collision of smooth spheres.
Week
5

Module 5:

4h

Unit 1: Newton's Law of Motion

4 study hours
  • •State Newton's laws of motion and apply them to solve problems.
  • •Define force and solve problems involving forces acting on a particle.
  • •Apply Newton's laws to describe the motion of a particle in space.
Week
6

Module 5:

4h

Unit 2: Work, Power and Energy

3 study hours
  • •Define work, power, and energy and solve related problems.
  • •Apply the principle of linear momentum to solve problems.
  • •Apply the principle of angular momentum to solve problems.

Unit 3: Rectilinear Motion

1 study hours
  • •Define rectilinear motion and solve problems involving uniform force fields.
  • •Explain uniformly accelerated motion and solve related problems.
  • •Define weight and acceleration due to gravity and apply them in calculations.
Week
7

Module 6:

4h

Unit 1: Reduction of Coplanar Forces Acting on a Rigid Body to a Force and a Couple

4 study hours
  • •Reduce coplanar forces acting on a rigid body to a single force and a single couple.
  • •Calculate the center of mass of simple bodies.
  • •Analyze the motion of the center of mass.
Week
8

Module 6:

4h

Unit 2: Moment of a Force

4 study hours
  • •Define the moment of a force and solve related problems.
  • •Explain the concept of couples and their properties.
  • •Apply the conditions for equilibrium of a particle to solve problems.
Week
9

Module 7:

4h

Unit 1: The Hamiltonian

4 study hours
  • •Define the Hamiltonian and state Hamilton's equations.
  • •Explain ignorable or cyclic coordinates and their significance.
  • •Define phase space and state Liouville's theorem.
Week
10

Module 7:

4h

Unit 2: The Calculus of Variation

4 study hours
  • •Define the calculus of variation and state Hamilton's principle.
  • •Explain canonical or contact transformations.
  • •Determine the condition for a transformation to be canonical.
Week
11

Module 7:

4h

Unit 3: The Hamilton-Jacobi Equation

4 study hours
  • •State the Hamilton-Jacobi equation and solve it for simple systems.
  • •Analyze cases where the Hamiltonian is independent of time.
  • •Define phase integrals, action, and angle variables.
Week
12

Review

4h

Review: Modules 1-4

4 study hours
  • •Review all modules
  • •Work on assignments
Week
13

Review

4h

Review: Modules 5-7

4 study hours
  • •Review all modules
  • •Work on assignments

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

Read the complete course material as provided by NOUN.

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Thoroughly review all worked examples in the study units.

2

Practice solving problems from the TMAs and self-assessment exercises.

3

Create concept maps linking Lagrange's equations, Hamilton's equations, and conservation laws.

4

Focus on understanding the applications of each principle rather than just memorizing formulas.

5

Allocate sufficient time to practice solving problems involving constraints and impulsive motion.

6

Review past exam papers to familiarize yourself with the question formats and difficulty level.

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