Analytical Dynamics - Lagrangian and 3D Rigid Body Dynamics
Comprehensive exploration of analytical dynamics, covering Lagrangian mechanics and 3D rigid body motion. Extends knowledge beyond undergraduate level, focusing on deriving equations of motion and analyzing system behavior.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.