Lagrangian Mechanics Courses and Certifications

Dot Physics

Lagrangian Mechanics - Motion Along Straight, Circular and Parabolic Paths

Explore Lagrangian mechanics through practical examples, modeling frictionless bead motion along straight, circular, and parabolic paths using Python simulations.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Dot Physics

Lagrangian Mechanics - Using Lagrange Multipliers to Find Forces of Constraint

Explore how Lagrange multipliers determine constraint forces in mechanical systems, focusing on the Half Atwood Machine example and tension calculation methods.

• YouTube
• 19 minutes
• Self-Paced
• Free Video

Dot Physics

Lagrangian Mechanics - Mass Sliding Off a Frictionless Sphere Using Lagrange Multipliers

Explore the physics of a mass sliding off a frictionless sphere through Lagrangian mechanics and Lagrange multipliers, with practical Python implementation and visual demonstrations.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Analytical Mechanics for Spacecraft Dynamics

12 ratings at Coursera

Derive spacecraft equations of motion efficiently: D'Alembert's principle and virtual work, Kane's equations, Lagrange's equations with multipliers for Pfaffian constraints, and Hamilton's extended principle for flexible bodies.

• Coursera
• 3 weeks, 11 hours a week
• Self-Paced
• Paid Course

Engineering Dynamics

10 ratings

This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems.

• MIT OpenCourseWare
• 40 hours
• Self-Paced
• Free Video

Mathemaniac

The Action Principle Explained: Finding Satisfaction in Physics

Delve into the action principle in physics, exploring why this seemingly arbitrary quantity should be minimized and discovering a more intuitive understanding of this fundamental concept.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Principle of Least Action and Lagrange's Equations of Mechanics - Basics of Calculus of Variations

Explore how the principle of stationary action yields Newton’s and Euler–Lagrange equations, with applications to the brachistochrone and cubic spline curves.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Kane's Method, Kane's Equations, Avoiding Lagrange Multipliers - Quasivelocities & Dynamic Equations

Learn how quasivelocities and Kane’s method eliminate Lagrange multipliers when deriving constrained mechanical systems’ equations of motion.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Lagrange Multipliers and Constraint Forces - Nonholonomic Constraints - Downhill Race Various Shapes

Derive constraint forces with Lagrange multipliers, then apply nonholonomic dynamics to wheeled systems and rolling bodies in a downhill race.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Lagrange’s Equations with Conservative and Non-Conservative Forces - Phase Space Introduction

Derive Lagrange’s equations for conservative and non-conservative forces, extend them to rigid bodies, and analyze motion through phase space and phase portraits.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Lagrange's Equations from D’Alembert’s Principle - Worked Examples

Derive Lagrange’s equations from D’Alembert’s principle and apply them to baton, cart-pendulum, and spring-mass systems.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

D’Alembert’s Principle of Virtual Work - Active Forces and Workless Constraint Forces

Derive D’Alembert’s principle of virtual work by separating active forces from workless constraint forces.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Lagrange's Equations Introduction - Generalized Coordinates, Constraints, Degrees of Freedom

Introduces Lagrangian mechanics through generalized coordinates, holonomic and nonholonomic constraints, and the counterintuitive instability of a shopping cart.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

NPTEL;  IIT Kharagpur

Classical Mechanics - From Newtonian to Lagrangian Formulation

This course deals with the fundamentals of classical mechanics. Mechanics is one of the core subjects for physics and engineering disciplines. This course starts from the basics of Newtonian mechanics.

• YouTube
• 1 day 9 hours
• Self-Paced
• Free Video

Ross Dynamics Lab

Rolling Coin, Bicycles, Fish, Chaplygin Swimmer - Small Oscillations About Equilibrium

Explores nonholonomic motion through rolling coins, bicycles, fish, and rattlebacks, then derives normal modes and natural frequencies for small oscillations.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video