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#Analytical Dynamics

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Analytical Dynamics - Lagrangian and 3D Rigid Body Dynamics

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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.
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29 Lesons
1 day 10 hours
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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8 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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8 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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10 Lesons
59 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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7 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.
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6 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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6 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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9 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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6 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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5 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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7 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Ross Dynamics Lab

Planar Kinematics & Dynamics of a Particle

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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.
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5 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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8 Lesons
55 minutes
On-Demand
Free-Video
Ross Dynamics Lab

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

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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.
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8 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Ross Dynamics Lab

Normal Modes of Mechanical Systems - Oscillations and Instabilities

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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.
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6 Lesons
1 hour 6 minutes
On-Demand
Free-Video