Spring Forces
Learn to simulate spring forces using vectors and create oscillating motion in p5.js. Explore Hooke's Law, particle systems, and advanced techniques for realistic spring animations.
Lagrangian Coherent Structures Introduction
Explore Lagrangian coherent structures in fluid flows, revealing particle transport patterns. Learn theoretical foundations and applications in fluid mechanics, with insights on reduced order modeling.
Gravity Gradient - Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station
Explore gravity gradient effects on spacecraft stability, including Euler equations, pitch stability, torque equilibrium angles, and applications to the International Space Station.
Dual-Spin Spacecraft - Instability of Intermediate and Minimum Principal Axes for Free Rigid Bodies
Explore dual-spin spacecraft stabilization, intermediate axis instability, and long-term minimum axis instability. Learn about historical space missions and passive attitude stability techniques.
Euler's Equations of Rigid Body Dynamics Derived - Qualitative Analysis - Build Rigid Body Intuition
Comprehensive exploration of Euler's equations for rigid body dynamics, covering derivation, analysis, and practical applications through various examples like spinning tops and fidget spinners.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Double Pendulum
Simulate a double pendulum in Processing (Java) with step-by-step guidance. Learn to implement formulas, visualize motion, and add path tracing and damping effects.
Cube Wave by Bees and Bombs
Learn to recreate a mesmerizing 3D cube wave animation using p5.js and WebGL. Explore oscillation, 3D rendering, and perspective techniques to bring this hypnotic visual effect to life.
More Inverse Kinematics and Texturing Cloth Simulation
Explore advanced inverse kinematics techniques and learn to texture 3D cloth simulations in Processing. Gain hands-on experience with multiple snake models, fixed points, and meshed cloth texturing.