Ross Dynamics Lab Courses

Center of Mass and Moment of Inertia Matrix - Example Calculations

Example calculations for center of mass and moment of inertia matrix in space vehicle dynamics. Covers planar rigid bodies, composite shapes, and practical applications using integrals and common approximation methods.

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

Moment of Inertia Matrix and Principal Axis Frame - MATLAB Example Calculation

Explore moment of inertia matrix calculation, principal axis frame, and their significance in rigid body dynamics. Includes MATLAB demonstration for practical application in spacecraft attitude control.

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

Euler Angle Simulation with MATLAB - Integrating the Rotational Kinematic Differential Equations

Simulate rigid body orientation using Euler angles and MATLAB. Learn to integrate kinematic differential equations, visualize results, and explore alternative attitude coordinates like quaternions.

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

Quaternions for Rotation, Axis-Angle, Euler Parameters - MATLAB Examples - Rodrigues Rotation Formula

Explore quaternions, axis-angle representation, and Euler parameters for 3D rotations. Learn to calculate and convert between different rotation formats using MATLAB examples and tutorials.

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

Hamilton-Jacobi Theory - Finding the Best Canonical Transformation + Examples

Explore Hamilton-Jacobi theory for optimal canonical transformations in Hamiltonian systems. Learn to solve the Hamilton-Jacobi equation and apply it to oscillators and central force problems.

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

Worked Example of 2 Particle System - MATLAB Tutorial - Implications of Energy and Momentum Conservation

Detailed analysis of a two-particle spring system, exploring conservation laws and using MATLAB to solve complex dynamics problems in space vehicle motion.

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

Generating Function of a Canonical Transformation - Examples and the Big Picture

Explore generating functions for canonical transformations in Hamiltonian systems. Learn about harmonic oscillator examples, near-identity transformations, and connections to quantum mechanics and gauge invariance.

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

Kinetic Energy - Where Does It Come From? - Linear and Angular Momentum - Worked Examples

Explore kinetic energy, linear and angular momentum, and their applications in space vehicle dynamics. Gain insights into energy conservation, pendulum motion, and momentum rate equations.

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

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

Explore variational principles in mechanics, including the Principle of Least Action and Lagrange's equations. Learn calculus of variations techniques and their applications in physics and engineering problems.

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

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