Ross Dynamics Lab Courses

Friction and Phase Portraits - Coulomb Friction - Cone of Friction - Falling Broom - Spinning Top

Explore Coulomb friction, phase portraits, and 3D rigid body dynamics. Analyze friction effects on equilibrium, falling objects, and spinning tops using experiments and mathematical models.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Chaos in Mechanical Systems, Routh Procedure, Ignorable Coordinates and Symmetries - Noether's Theorem

Explore chaotic dynamics, Routhian method, and Noether's theorem in mechanical systems. Learn about ignorable coordinates, constants of motion, and their relation to physical symmetries through various examples.

• YouTube
• 59 minutes
• On-Demand
• Free Video

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

Explore Lagrange multipliers, constraint forces, and nonholonomic constraints in analytical dynamics. Analyze examples like rigid rods, roller racers, and rolling disks to understand generalized forces and their Newtonian connections.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Phase Portraits from Potential Energy - Bifurcations - Constraint Forces from Lagrange Multipliers

Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

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

Explore Lagrange's equations for conservative and non-conservative forces, rigid body systems, and phase space analysis. Learn to solve and classify motions using advanced analytical dynamics techniques.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

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

Explore D'Alembert's Principle and Lagrange's Equations through worked examples, including baton sliding, cart-pendulum system, and spring-mass system. Learn to formulate equations of motion for multiparticle systems.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

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

Explore D'Alembert's Principle of Virtual Work, analyzing active forces and workless constraint forces in analytical dynamics. Gain insights into nonholonomic constraints and multiparticle systems.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

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

Comprehensive introduction to Lagrangian mechanics, covering generalized coordinates, constraints, and degrees of freedom. Explores holonomic and nonholonomic constraints, with examples including the intriguing shopping cart instability.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Rigid Body Dynamics - Stability About Principal Axes - Qualitative Analysis of Spinning Objects

Explore rigid body dynamics, stability of principal axes, and qualitative analysis of spinning objects. Understand the tennis racket theorem and intermediate axis instability through demonstrations and intuitive explanations.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Rigid Body Kinematic Differential Equation for Euler Angles and Rotation Matrix

Comprehensive exploration of rigid body kinematics, focusing on Euler angles, rotation matrices, and differential equations. Covers singularities, alternatives, and applications in free rigid body motion analysis.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Rotational Dynamics About an Arbitrary Reference Point - Planar Rigid Body Motion - Car Jump Example

Explore rotational dynamics of rigid bodies using arbitrary reference points, with applications to car jumps and planar motion. Covers angular momentum, Euler's equations, and moment of inertia concepts.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Newton-Euler Equations for a Rigid Body - Center of Mass & Inertia Tensor Calculation Worked Example

Comprehensive exploration of rigid body dynamics, covering mass distribution, center of mass calculation, Newton-Euler equations, and rotational motion, with practical examples and mathematical formulations.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Tetherball, Angular Momentum, and Central Forces - Indiana Jones's Whip, Snake Wrapping Around a Tree

Explore tetherball dynamics, angular momentum, and central forces through real-world examples like Indiana Jones's whip and tree snakes. Learn to solve nonlinear ODEs and analyze spring-mass systems in the plane.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Planar Kinematics & Dynamics of a Particle

Explore planar kinematics and particle dynamics, covering projectile motion, pendulums, polar coordinates, and the transport equation for rotating frames. Gain insights into 2D motion analysis.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Normal Forms for Vector Fields

Introduction to normal forms for vector fields, focusing on simplifying nonlinear terms and determining topological equivalence. Covers theory, examples, and applications in dynamical systems analysis.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video