Ross Dynamics Lab Courses

Single Particle Dynamics - 1D and 2D Worked Examples

Explore single particle dynamics through 1D and 2D examples, covering conservative forces, Newton's laws, projectile motion, and pendulum equations. Gain insights into space vehicle dynamics.

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

Transport Theorem Worked Examples - Vector Derivatives When Frames Are Rotating and Translating

Comprehensive exploration of vector derivatives in rotating and translating frames, with practical examples. Covers transport theorem, matrix representations, and applications to space vehicle dynamics.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Satellite Reference Frames, Viewing Geometry, and Mission Analysis

Explore spacecraft reference frames, mission analysis basics, and satellite viewing geometry. Learn about ECI, ECEF, orbital frames, and key concepts like sub-satellite points, access areas, and ground tracks.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Hamiltonian Systems Introduction - Why Study Them?

Explore Hamiltonian systems and their advantages in mechanics. Learn about generalized momentum, canonical equations, and the transformation from Lagrangian to Hamiltonian formalism.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Bifurcations in 2D, Part 4 - Global Bifurcations, Limit Cycle Creation - Homoclinic Bifurcation

Explores global bifurcations in 2D systems, focusing on limit cycle creation through saddle-node, SNIPER, and homoclinic bifurcations. Examines universal behaviors and applications to biological systems.

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

Bifurcations in 2D, Part 1 - Introduction, Saddle-Node, Pitchfork, Examples

Explore bifurcations in 2D systems, including saddle-node and pitchfork types. Learn how fixed points and closed orbits change with parameter variations, using examples from genetic regulatory systems.

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

Limit Cycles - Poincare-Bendixson Worked Examples: Glycolysis

Explore Poincaré-Bendixson theorem applications in limit cycle analysis, including a glycolysis model. Learn to construct trapping regions using nullclines and understand parameter spaces for stable limit cycles.

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

Insect Outbreak Model - A Cusp Catastrophe Population Dynamics Example

Explore insect outbreak modeling using cusp catastrophe theory, analyzing population dynamics, fixed points, and bifurcations in a budworm-fir tree ecosystem.

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

Coupled Rigid Bodies, Impulsive Dynamics, Applications - Trap Jaw Ants, Leaping Lizards, Falling Cat

Explore advanced dynamics applications in biology, from cat landings to flying snakes. Discover how angular momentum and impulsive dynamics explain fascinating natural phenomena and inspire robotic designs.

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

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

Introduces Kane's method for efficient modeling of constrained systems using quasivelocities, avoiding Lagrange multipliers. Covers theoretical foundations and practical examples like vehicle stability and semi-truck dynamics.

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

Normal Modes of Mechanical Systems - Oscillations and Instabilities

Explore normal modes in mechanical systems, including oscillatory patterns, steady drift, and instability. Learn about natural frequencies, mode shapes, and their applications in analyzing system responses to forcing.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

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

Explore nonholonomic systems and small oscillations in analytical dynamics. Analyze rolling coins, bicycle stability, and aquatic locomotion. Learn about normal modes and natural frequencies in multi-degree freedom systems.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video