Ross Dynamics Lab Courses

Kalman Filter for Beginners - Recursive Filters & MATLAB Examples

4 ratings

See how recursive averaging and moving-average and low-pass filters smooth noisy data, with MATLAB demonstrations leading into the basics of the Kalman Filter.

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

Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

2 ratings

Explore how saddle-node, transcritical, pitchfork, period-doubling, and Hopf bifurcations change dynamical-system phase portraits as parameters vary.

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

Lagrangian Coherent Structures Introduction

Explore how Lagrangian coherent structures reveal particle-transport patterns in fluid flows, from vortices and hurricanes to reduced-order models.

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

Gravity Gradient - Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station

Analyzes gravity-gradient attitude stability using Euler’s rigid-body equations, deriving pitch, roll, and yaw conditions, oscillation frequencies, torque equilibrium, and ISS implications.

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

Dual-Spin Spacecraft - Instability of Intermediate and Minimum Principal Axes for Free Rigid Bodies

Analyze free rigid-body instabilities and derive how a flywheel stabilizes spacecraft rotation about any principal axis.

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

Euler's Equations of Rigid Body Dynamics Derived - Qualitative Analysis - Build Rigid Body Intuition

Derives Euler’s equations in a body-fixed frame and uses tops, wheels, spinners, and simulations to build intuition for free rigid-body motion.

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

Center of Mass and Moment of Inertia Matrix - Example Calculations

Calculate center of mass and moment-of-inertia matrices for planar and three-dimensional rigid bodies using integrals and composite-body approximations.

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

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

Derive a rigid body's inertia matrix and use MATLAB eigenanalysis to construct its principal-axis frame.

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

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

Simulate rigid-body orientation from time-varying angular velocity by integrating Euler-angle kinematic equations in MATLAB and visualizing the motion.

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

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

Explore axis-angle rotation and Euler parameters for rigid-body orientation, with MATLAB demonstrations converting between rotation matrices, quaternions, and angular representations.

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

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

Derives Hamilton–Jacobi theory for constructing canonical transformations, with applications to the harmonic oscillator and Kepler problem.

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

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

Worked example of a two-particle spring system using center-of-mass dynamics, conservation laws, polar coordinates, and MATLAB.

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

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

Explore how generating functions construct canonical transformations in Hamiltonian mechanics, with harmonic oscillator and Hamiltonian-flow examples.

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

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

Explains kinetic energy and conservation intuitively, then applies linear and angular momentum rate equations to fixed- and moving-pivot pendulums.

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

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