Канал: Dr. Shane Ross

Saharan Dust Crossing the Atlantic: Atmospheric Structures Shaping the Godzilla Dust Plume

Saharan Dust Crossing the Atlantic: Atmospheric Structures Shaping the Godzilla Dust Plume

Professor Rambling in Engineering Class, Part 2 #space #physics

Professor Rambling in Engineering Class, Part 2 #space #physics

Chaotic Waterwheel Illustrating Lorenz Equations #chaos #physics #demonstration

Chaotic Waterwheel Illustrating Lorenz Equations #chaos #physics #demonstration

Trajectories with Prescribed Itineraries and MATLAB Tutorial, 3-Body Problem Topic 15

Trajectories with Prescribed Itineraries and MATLAB Tutorial, 3-Body Problem Topic 15

Orbital Motion in Cislunar Space

Orbital Motion in Cislunar Space

Probability Machine - Galton Board Plinko in Slow Motion with Bell Curve Distribution #statistics

Probability Machine - Galton Board Plinko in Slow Motion with Bell Curve Distribution #statistics

3-Body Problem Periodic Orbits & Stable Manifolds using Differential Correction, MATLAB | Topic 14

3-Body Problem Periodic Orbits & Stable Manifolds using Differential Correction, MATLAB | Topic 14

Professor Rambling in Engineering Class, Part 13 #spacecraft #physics #orbitalmechanics

Professor Rambling in Engineering Class, Part 13 #spacecraft #physics #orbitalmechanics

Global Orbit Structure in the 3-Body Problem: Theorem and Examples | Topic 13

Global Orbit Structure in the 3-Body Problem: Theorem and Examples | Topic 13

Find Your Latitude Using Stars

Find Your Latitude Using Stars

Motion Near L4, L5 Lagrange Points- Tadpole, Horseshoe Orbit, Trojan Asteroids,Lucy Mission,Topic 12

Motion Near L4, L5 Lagrange Points- Tadpole, Horseshoe Orbit, Trojan Asteroids,Lucy Mission,Topic 12

Math potatoes and gravy

Math potatoes and gravy

Slime Mold vs. LEGO Maze: Nature's Mind-Boggling Intelligence!

Slime Mold vs. LEGO Maze: Nature's Mind-Boggling Intelligence!

Kalman Filter for Beginners, Part 3- Attitude Estimation, Gyro, Accelerometer, Velocity MATLAB Demo

Kalman Filter for Beginners, Part 3- Attitude Estimation, Gyro, Accelerometer, Velocity MATLAB Demo

Kalman Filter for Beginners, Part 2 - Estimation and Prediction Process & MATLAB Example

Kalman Filter for Beginners, Part 2 - Estimation and Prediction Process & MATLAB Example

Kalman Filter for Beginners, Part 1 - Recursive Filters & MATLAB Examples

Kalman Filter for Beginners, Part 1 - Recursive Filters & MATLAB Examples

Trajectory Types Near L1, L2, & L3 in the Three Body Problem - Theory and MATLAB Examples | Topic 11

Trajectory Types Near L1, L2, & L3 in the Three Body Problem - Theory and MATLAB Examples | Topic 11

Interstellar turkeys, epic version #shorts

Interstellar turkeys, epic version #shorts

Geometry of Motion near L1, L2, 3-Body Dynamical Systems Analysis, McGehee Representation | Topic 10

Geometry of Motion near L1, L2, 3-Body Dynamical Systems Analysis, McGehee Representation | Topic 10

Physics of Gliding Animals and Plants: Insights from Models, Experiments and Bio-inspired Designs

Physics of Gliding Animals and Plants: Insights from Models, Experiments and Bio-inspired Designs

Drone-Based Wind Measurements in Aquatic Environments

Drone-Based Wind Measurements in Aquatic Environments

Phones are Space Debris? #shorts

Phones are Space Debris? #shorts

Cislunar Space: 3-Body Model of Orbital Dynamics Beyond the Geosynchronous Belt (xGEO)

Cislunar Space: 3-Body Model of Orbital Dynamics Beyond the Geosynchronous Belt (xGEO)

'Asteroid' Impact? What Have We Unleashed? #shorts

'Asteroid' Impact? What Have We Unleashed? #shorts

Defunct Apollo Spacecraft Cycling Between Orbits Around Earth and Sun #shorts

Defunct Apollo Spacecraft Cycling Between Orbits Around Earth and Sun #shorts

Better Call Shane

Better Call Shane

Motion Near L1 and L2: Linearized Equations of Motion in the 3-Body Problem | Topic 9

Motion Near L1 and L2: Linearized Equations of Motion in the 3-Body Problem | Topic 9

Earth to Venus Trajectory Using NO Propulsion - Matt Werner Thesis Defense

Earth to Venus Trajectory Using NO Propulsion - Matt Werner Thesis Defense

Transition Tube in Phase Space #shorts

Transition Tube in Phase Space #shorts

Calculating Collinear Lagrange Point Positions: L1, L2, L3 in Restricted 3-Body Problem | Topic 8

Calculating Collinear Lagrange Point Positions: L1, L2, L3 in Restricted 3-Body Problem | Topic 8

Lagrange Points L4, L5 in 3-Body Problem: Derivation of Equilateral Point Location | Topic 7

Lagrange Points L4, L5 in 3-Body Problem: Derivation of Equilateral Point Location | Topic 7

3-Body Problem Jacobi Constant, Zero Velocity Curves, Hill Regions of Possible Motion | Topic 6

3-Body Problem Jacobi Constant, Zero Velocity Curves, Hill Regions of Possible Motion | Topic 6

Fluid Dynamics on a Möbius Strip #shorts

Fluid Dynamics on a Möbius Strip #shorts

3 Body Problem Hamilton's Equations -&- Why View Motion in a Rotating Frame? | Topic 5

3 Body Problem Hamilton's Equations -&- Why View Motion in a Rotating Frame? | Topic 5

From Earth to Any Planet for FREE?

From Earth to Any Planet for FREE?

3-Body Problem Lagrangian Equations and Effective Potential Energy | Topic 4

3-Body Problem Lagrangian Equations and Effective Potential Energy | Topic 4

3-Body Problem Equations Derived, Part 2: Rotating Frame | Topic 3

3-Body Problem Equations Derived, Part 2: Rotating Frame | Topic 3

3-Body Problem Equations Derived, Part 1: Inertial Frame and Non-dimensionalization | Topic 2

3-Body Problem Equations Derived, Part 1: Inertial Frame and Non-dimensionalization | Topic 2

Three Body Problem Introduction: Lecture 1 of a Course Series | Topic 1

Three Body Problem Introduction: Lecture 1 of a Course Series | Topic 1

How Microbes Cross the Air-Water Interface from Harmful Algal Blooms & the Water Cycle

How Microbes Cross the Air-Water Interface from Harmful Algal Blooms & the Water Cycle

Vortex Ring and Air Mass Boundaries #shorts

Vortex Ring and Air Mass Boundaries #shorts

Lagrangian Coherent Structures Introduction

Lagrangian Coherent Structures Introduction

Geometry of Transition Dynamics in 3 Degrees of Freedom Systems with Energy Dissipation #shorts

Geometry of Transition Dynamics in 3 Degrees of Freedom Systems with Energy Dissipation #shorts

Space Isn't Empty #shorts

Space Isn't Empty #shorts

Time Series Analysis Introduction

Time Series Analysis Introduction

The Big Yellow One Is the Sun #shorts

The Big Yellow One Is the Sun #shorts

Repairing James Webb Space Telescope at Lunar Gateway Station #shorts

Repairing James Webb Space Telescope at Lunar Gateway Station #shorts

Preserve the Moon's Far Side? #shorts

Preserve the Moon's Far Side? #shorts

Space Shuttles in Love #shorts

Space Shuttles in Love #shorts

Muffins or Chihuahuas? #shorts

Muffins or Chihuahuas? #shorts

Clustering, Classification & Data Visualization

Clustering, Classification & Data Visualization

OUT-OF-CONTROL Spin & Astronauts' Reaction #shorts

OUT-OF-CONTROL Spin & Astronauts' Reaction #shorts

Don't Use the Rainbow Color Map

Don't Use the Rainbow Color Map

Tube Highway to L2 Halo Orbit- James Webb Orbit #shorts

Tube Highway to L2 Halo Orbit- James Webb Orbit #shorts

Effective Use of Graphs- Data Visualization, Part 1

Effective Use of Graphs- Data Visualization, Part 1

Poehler Coordinates #shorts

Poehler Coordinates #shorts

3-Body Problem- New Space Mission Ideas

3-Body Problem- New Space Mission Ideas

Orbital Debris: Is It Too Late?

Orbital Debris: Is It Too Late?

Red Tide Respiratory Forecast

Red Tide Respiratory Forecast

Interstellar Docking Scene Analyzed by Engineer

Interstellar Docking Scene Analyzed by Engineer

Control Moment Gyroscopes & Falling Cats: Attitude Control

Control Moment Gyroscopes & Falling Cats: Attitude Control

Gravity Gradient, Part 4, Space Shuttle, Asteroids, and the Moon

Gravity Gradient, Part 4, Space Shuttle, Asteroids, and the Moon

Gravity Gradient, Part 3, Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station

Gravity Gradient, Part 3, Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station

Gravity Gradient, Part 2, Equilibrium Orientations

Gravity Gradient, Part 2, Equilibrium Orientations

Gravity Gradient, Part 1, Deriving the Gravity Gradient Torque on a Body in Orbit

Gravity Gradient, Part 1, Deriving the Gravity Gradient Torque on a Body in Orbit

Dual-Spin Spacecraft, Stabilizing Rotation About Any Principal Axis

Dual-Spin Spacecraft, Stabilizing Rotation About Any Principal Axis

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

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

Chaotic Atmospheric Dynamics, Hurricanes & Disease Spread

Chaotic Atmospheric Dynamics, Hurricanes & Disease Spread

Free Rigid Body Motion | Precession of Symmetric Bodies | General Motion

Free Rigid Body Motion | Precession of Symmetric Bodies | General Motion

Can Science be Trusted? A Scientist's Perspective on Peer Review, Bias, Consensus, & Reproducibility

Can Science be Trusted? A Scientist's Perspective on Peer Review, Bias, Consensus, & Reproducibility

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

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

Center of Mass & Moment of Inertia Matrix | Example Calculations

Center of Mass & Moment of Inertia Matrix | Example Calculations

Mass Moments of a Rigid Body | Analog to Statistical Moments

Mass Moments of a Rigid Body | Analog to Statistical Moments

Moment of Inertia Matrix & Principal Axis Frame | MATLAB Example Calculation

Moment of Inertia Matrix & Principal Axis Frame | MATLAB Example Calculation

Attitude Determination, Davenport's q-Method for Optimal State Estimation | Theory & MATLAB Demo

Attitude Determination, Davenport's q-Method for Optimal State Estimation | Theory & MATLAB Demo

Attitude Determination | Spacecraft Sun Sensors, Magnetometers | TRIAD Method & MATLAB Tutorial

Attitude Determination | Spacecraft Sun Sensors, Magnetometers | TRIAD Method & MATLAB Tutorial

How Far Can Cannabis Pollen Travel? Drone Sampling & Computer Models to Prevent Cross-Pollination

How Far Can Cannabis Pollen Travel? Drone Sampling & Computer Models to Prevent Cross-Pollination

Selection of Attitude Coordinates

Selection of Attitude Coordinates

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

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

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

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

Euler Angle Rates & Angular Velocity- Kinematic Differential Equation for Rigid Body Dynamics

Euler Angle Rates & Angular Velocity- Kinematic Differential Equation for Rigid Body Dynamics

Euler Angles for Aerospace | Yaw, Pitch, Roll

Euler Angles for Aerospace | Yaw, Pitch, Roll

Rigid Body Kinematics Introduction | Rotation Matrix Relating Frames in 3D | Direction Cosine Matrix

Rigid Body Kinematics Introduction | Rotation Matrix Relating Frames in 3D | Direction Cosine Matrix

Hamilton-Jacobi Theory: Finding the Best Canonical Transformation + Examples | Lecture 9

Hamilton-Jacobi Theory: Finding the Best Canonical Transformation + Examples | Lecture 9

Rigid System of Particles | Going to Continuous Limit

Rigid System of Particles | Going to Continuous Limit

Hamiltonian Flow is a Canonical Transformation | Strange Non-Intuitive Momenta | Lecture 8

Hamiltonian Flow is a Canonical Transformation | Strange Non-Intuitive Momenta | Lecture 8

Worked Example of 2 Particle System| MATLAB Tutorial| Implications of Energy & Momentum Conservation

Worked Example of 2 Particle System| MATLAB Tutorial| Implications of Energy & Momentum Conservation

System of Particles | Dynamics, Energy & Momenta

System of Particles | Dynamics, Energy & Momenta

Dynamics Modeling: An 8 Step Approach

Dynamics Modeling: An 8 Step Approach

Generating Function of a Canonical Transformation | Examples and the Big Picture | Lecture 7

Generating Function of a Canonical Transformation | Examples and the Big Picture | Lecture 7

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

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

Principle of Least Action, Lagrange's Equations of Mechanics | Calculus of Variations | Lecture 6

Principle of Least Action, Lagrange's Equations of Mechanics | Calculus of Variations | Lecture 6

Single Particle Dynamics | 1D and 2D Worked Examples

Single Particle Dynamics | 1D and 2D Worked Examples

Rigid Body Dynamics Overview | Multi-particle System to Continuous Rigid Mass Distribution

Rigid Body Dynamics Overview | Multi-particle System to Continuous Rigid Mass Distribution

Moon's Velocity & Acceleration with Respect to Sun | Worked Example with Kinematic Transport Theorem

Moon's Velocity & Acceleration with Respect to Sun | Worked Example with Kinematic Transport Theorem

Canonical Transformations | Hamiltonian Changes of Variables | Symplectomorphisms | Lecture 5

Canonical Transformations | Hamiltonian Changes of Variables | Symplectomorphisms | Lecture 5

Worked Examples Using Transport Theorem | Kinematics with Rotating Frames

Worked Examples Using Transport Theorem | Kinematics with Rotating Frames

Hamiltonian Flow Poincare Integral Invariants| Ignorable/Cyclic Coordinates | Lecture 4

Hamiltonian Flow Poincare Integral Invariants| Ignorable/Cyclic Coordinates | Lecture 4

Transport Theorem Worked Examples | Vector Derivatives When Frames are Rotating and Translating

Transport Theorem Worked Examples | Vector Derivatives When Frames are Rotating and Translating

Coordinate Frames, Rotating Frames | Transport Theorem Introduced | Cylindrical, Spherical Frames

Coordinate Frames, Rotating Frames | Transport Theorem Introduced | Cylindrical, Spherical Frames

Hamiltonian System Properties | Classical Uncertainty Principle, 2D Fluid Streamfunctions, Lecture 3

Hamiltonian System Properties | Classical Uncertainty Principle, 2D Fluid Streamfunctions, Lecture 3

Satellite Reference Frames, Viewing Geometry, and Mission Analysis

Satellite Reference Frames, Viewing Geometry, and Mission Analysis

Legendre Transformation | Get Hamiltonian from Lagrangian | Spring Mass, Harmonic Oscillator, Lect 2

Legendre Transformation | Get Hamiltonian from Lagrangian | Spring Mass, Harmonic Oscillator, Lect 2

Space Vehicle Dynamics- What You Will Learn & Introduction to Instructor | Lecture 1 of Course

Space Vehicle Dynamics- What You Will Learn & Introduction to Instructor | Lecture 1 of Course

Hamiltonian Systems Introduction- Why Study Them? | Lecture 1 of a Course on Hamilton's Equations

Hamiltonian Systems Introduction- Why Study Them? | Lecture 1 of a Course on Hamilton's Equations

Professor Shane Ross Introduction

Professor Shane Ross Introduction

Harmful Algal Blooms | Forecasting Respiratory Irritation Due to Red Tide Exposure 1 Day Ahead

Harmful Algal Blooms | Forecasting Respiratory Irritation Due to Red Tide Exposure 1 Day Ahead

Horseshoe Map - Essence of Chaos, Symbolic Dynamics, and the Shift Map

Horseshoe Map - Essence of Chaos, Symbolic Dynamics, and the Shift Map

Separatrix Splitting Leads to Chaos via Homoclinic Tangle | Forced Double-Well Oscillator Example

Separatrix Splitting Leads to Chaos via Homoclinic Tangle | Forced Double-Well Oscillator Example

Fractal Basin Boundary in Forced Double-Well Oscillator

Fractal Basin Boundary in Forced Double-Well Oscillator

Experimental strange attractors | forced double-well oscillator

Experimental strange attractors | forced double-well oscillator

Henon Map- Strange Attractor with Fractal Microstructure

Henon Map- Strange Attractor with Fractal Microstructure

Baker's Map- Simple 2D Map with a Fractal Chaotic Attractor

Baker's Map- Simple 2D Map with a Fractal Chaotic Attractor

Geometry of Strange Attractors: Chaos From Stretching and Folding in Phase Space

Geometry of Strange Attractors: Chaos From Stretching and Folding in Phase Space

Fractal Dimension - Box-Counting & Correlation Dimension

Fractal Dimension - Box-Counting & Correlation Dimension

Fractals: Koch Curve, Cantor Set, Non-Integer Dimension

Fractals: Koch Curve, Cantor Set, Non-Integer Dimension

Universality in Transitions to Chaos | Where Feigenbaum Constant δ=4.669 Comes From

Universality in Transitions to Chaos | Where Feigenbaum Constant δ=4.669 Comes From

Renormalization Theory for Dynamical Systems | Feigenbaum's Analysis of Period-Doubling Universality

Renormalization Theory for Dynamical Systems | Feigenbaum's Analysis of Period-Doubling Universality

Period-Doubling Route to Chaos | Universality, Experiments, ODEs, and Maps

Period-Doubling Route to Chaos | Universality, Experiments, ODEs, and Maps

Logistic Map, Part 3: Bifurcation Point Analysis | Bottlenecks in Maps, Intermittency Chaos

Logistic Map, Part 3: Bifurcation Point Analysis | Bottlenecks in Maps, Intermittency Chaos

Logistic Map, Part 2: Bifurcation Diagram and Self-Similarity

Logistic Map, Part 2: Bifurcation Diagram and Self-Similarity

Logistic Map, Part 1: Period Doubling Route to Chaos

Logistic Map, Part 1: Period Doubling Route to Chaos

Maps, Discrete Time Dynamical Systems - Introduction and Use

Maps, Discrete Time Dynamical Systems - Introduction and Use

Dynamics on Lorenz Attractor | Lorenz Map, Cobweb Diagrams

Dynamics on Lorenz Attractor | Lorenz Map, Cobweb Diagrams

Lorenz System Bifurcation Diagram- Exploring Parameter Space

Lorenz System Bifurcation Diagram- Exploring Parameter Space

Chaotic Attractors: a Working Definition of Chaos and Strange Attractors

Chaotic Attractors: a Working Definition of Chaos and Strange Attractors

Lyapunov Exponents & Sensitive Dependence on Initial Conditions

Lyapunov Exponents & Sensitive Dependence on Initial Conditions

Lorenz Attractor- How It Was Found

Lorenz Attractor- How It Was Found

Lorenz Equations Fixed Point Analysis

Lorenz Equations Fixed Point Analysis

Lorenz Equations Properties: Volume Contraction and Symmetry

Lorenz Equations Properties: Volume Contraction and Symmetry

3D Systems, Lorenz Equations Derived, Chaotic Waterwheel

3D Systems, Lorenz Equations Derived, Chaotic Waterwheel

Coupled Oscillators, Quasiperiodicity, Synchronization, Flows on the Torus

Coupled Oscillators, Quasiperiodicity, Synchronization, Flows on the Torus

Bifurcations in 2D, Part 4: Global Bifurcations, Limit Cycle Creation | Homoclinic Bifurcation

Bifurcations in 2D, Part 4: Global Bifurcations, Limit Cycle Creation | Homoclinic Bifurcation

Bifurcations in 2D, Part 3: Hopf Bifurcation Physical Examples

Bifurcations in 2D, Part 3: Hopf Bifurcation Physical Examples

Bifurcations in 2D, Part 2: Hopf Bifurcation- Birth of a Limit Cycle from a Fixed Point

Bifurcations in 2D, Part 2: Hopf Bifurcation- Birth of a Limit Cycle from a Fixed Point

Bifurcations in 2D, Part 1: Introduction, Saddle-Node, Pitchfork, Examples

Bifurcations in 2D, Part 1: Introduction, Saddle-Node, Pitchfork, Examples

3D-Printed Bio-Inspired Microfliers- Autorotating Maple Seeds

3D-Printed Bio-Inspired Microfliers- Autorotating Maple Seeds

Averaging Theory for Weakly Nonlinear Oscillators

Averaging Theory for Weakly Nonlinear Oscillators

Limit Cycles, Part 5: Van der Pol Oscillator, Weakly Nonlinear Limit | Energy Method

Limit Cycles, Part 5: Van der Pol Oscillator, Weakly Nonlinear Limit | Energy Method

Limit Cycles, Part 4: Van der Pol Equation, Strongly Nonlinear Limit, Relaxation Oscillations

Limit Cycles, Part 4: Van der Pol Equation, Strongly Nonlinear Limit, Relaxation Oscillations

Limit Cycles, Part 3: Poincare-Bendixson Worked Examples- Glycolysis

Limit Cycles, Part 3: Poincare-Bendixson Worked Examples- Glycolysis

Limit Cycles, Part 2: Analytical Tests for Limit Cycles- Lyapunov Functions, Dulac's Criterion

Limit Cycles, Part 2: Analytical Tests for Limit Cycles- Lyapunov Functions, Dulac's Criterion

Wind-induced drift of irregularly shaped objects in the ocean, using drone technology

Wind-induced drift of irregularly shaped objects in the ocean, using drone technology

Limit Cycles, Part 1: Introduction & Examples

Limit Cycles, Part 1: Introduction & Examples

Index Theory for Dynamical Systems, Part 2: Poincaré-Hopf Index Theorem | You Can't Comb a Coconut

Index Theory for Dynamical Systems, Part 2: Poincaré-Hopf Index Theorem | You Can't Comb a Coconut

Index Theory for Dynamical Systems, Part 1: The Basics

Index Theory for Dynamical Systems, Part 1: The Basics

Conservative Systems - Nonlinear Systems with Special Structure, Part 3

Conservative Systems - Nonlinear Systems with Special Structure, Part 3

Hamiltonian Systems - Nonlinear Systems with Special Structure, Part 2

Hamiltonian Systems - Nonlinear Systems with Special Structure, Part 2

Gradient Systems - Nonlinear Differential Equations with Special Structure, Part 1

Gradient Systems - Nonlinear Differential Equations with Special Structure, Part 1

Phase Plane Analysis: Worked Example | Rabbits Vs. Sheep Species Competition, Population Biology

Phase Plane Analysis: Worked Example | Rabbits Vs. Sheep Species Competition, Population Biology

Nonlinear Systems: Fixed Points, Linearization, & Stability

Nonlinear Systems: Fixed Points, Linearization, & Stability

Love Dynamics: Coupled Equations of Coupling

Love Dynamics: Coupled Equations of Coupling

Classifying Fixed Points of 2D Systems

Classifying Fixed Points of 2D Systems

Phase Portrait Introduction- Pendulum Example

Phase Portrait Introduction- Pendulum Example

2D Nonlinear Systems Introduction- Bead in a Rotating Hoop, 2D Phase Space

2D Nonlinear Systems Introduction- Bead in a Rotating Hoop, 2D Phase Space

Flows on the Circle | Ghosts and Bottlenecks in Dynamical Systems

Flows on the Circle | Ghosts and Bottlenecks in Dynamical Systems

The Science of Insect Outbreaks: Exploring Population Dynamics with Cusp Catastrophe Modeling

The Science of Insect Outbreaks: Exploring Population Dynamics with Cusp Catastrophe Modeling

Cusp Catastrophe Theory

Cusp Catastrophe Theory

Bead in a Rotating Hoop, Part 2: High Damping Limit

Bead in a Rotating Hoop, Part 2: High Damping Limit

Nondimensionalization of Equations, Physics Example | Bead in the Hoop, Buckingham Pi Theorem

Nondimensionalization of Equations, Physics Example | Bead in the Hoop, Buckingham Pi Theorem

Bead in a Rotating Hoop, Part 1- Deriving Equations of Motion

Bead in a Rotating Hoop, Part 1- Deriving Equations of Motion

Bifurcations Part 4- Robustness of Bifurcations Under Perturbation

Bifurcations Part 4- Robustness of Bifurcations Under Perturbation

Bifurcations Part 3- Pitchfork Bifurcation

Bifurcations Part 3- Pitchfork Bifurcation

Bifurcations Part 2- Transcritical Bifurcation, Laser Model Example

Bifurcations Part 2- Transcritical Bifurcation, Laser Model Example

Bifurcations Part 1, Saddle-Node Bifurcation

Bifurcations Part 1, Saddle-Node Bifurcation

Impossibility of Oscillations in 1D Flows

Impossibility of Oscillations in 1D Flows

Population Growth- The Logistic Model

Population Growth- The Logistic Model

Graphical Analysis of 1D Nonlinear ODEs

Graphical Analysis of 1D Nonlinear ODEs

Nonlinear ODEs- General Framework of Autonomous Ordinary Differential Equations

Nonlinear ODEs- General Framework of Autonomous Ordinary Differential Equations

Big Picture of Dynamics & Its Applications

Big Picture of Dynamics & Its Applications

Nonlinear Dynamics & Chaos Introduction- Lecture 1 of a Course

Nonlinear Dynamics & Chaos Introduction- Lecture 1 of a Course

Jumping and Slam Dunking on the Moon

Jumping and Slam Dunking on the Moon

Coupled Rigid Bodies, Impulsive Dynamics, Trap Jaw Ants, Leaping Lizards, Falling Cat, Lecture 29

Coupled Rigid Bodies, Impulsive Dynamics, Trap Jaw Ants, Leaping Lizards, Falling Cat, Lecture 29

Kane's Method, Kane's Equations, Avoiding Lagrange Multipliers | Quasivelocities | Lecture 28

Kane's Method, Kane's Equations, Avoiding Lagrange Multipliers | Quasivelocities | Lecture 28

Normal Modes of Mechanical Systems | Oscillations and Instabilities | Lecture 27 of Course

Normal Modes of Mechanical Systems | Oscillations and Instabilities | Lecture 27 of Course

What Makes a Rolling Coin or Bicycle Stable? Small Oscillations About Equilibrium, Lecture 26

What Makes a Rolling Coin or Bicycle Stable? Small Oscillations About Equilibrium, Lecture 26

Academic genealogy, mathematics and mechanics | academic family tree going back 1,000 years

Academic genealogy, mathematics and mechanics | academic family tree going back 1,000 years

Phase Portraits & Coulomb Friction, Cone of Friction, Falling Broom Hybrid Models, Spin Top, Lect 25

Phase Portraits & Coulomb Friction, Cone of Friction, Falling Broom Hybrid Models, Spin Top, Lect 25

Chaos in Mechanical Systems, Routhian, Ignorable Coordinates & Symmetries, Noether's Theorem Lect 24

Chaos in Mechanical Systems, Routhian, Ignorable Coordinates & Symmetries, Noether's Theorem Lect 24

Constant of Motion, Ignorable Coordinate, Routh's Procedure, Spherical Pendulum Eqs Derived, Lect 23

Constant of Motion, Ignorable Coordinate, Routh's Procedure, Spherical Pendulum Eqs Derived, Lect 23

Lagrange Multipliers & Constraint Forces, Nonholonomic Constraints | Downhill Race Shapes | Lect 22

Lagrange Multipliers & Constraint Forces, Nonholonomic Constraints | Downhill Race Shapes | Lect 22

Phase Portrait via Potential Energy, Bifurcations, Constraint Forces & Lagrange Multipliers, Lect 21

Phase Portrait via Potential Energy, Bifurcations, Constraint Forces & Lagrange Multipliers, Lect 21

Lagrange’s Equations with Conservative & Non-Conservative Forces | Phase Space Intro | Lecture 20

Lagrange’s Equations with Conservative & Non-Conservative Forces | Phase Space Intro | Lecture 20

Lagrange's Equations from D’Alembert’s Principle- plus WORKED EXAMPLES | Lecture 19 of Course

Lagrange's Equations from D’Alembert’s Principle- plus WORKED EXAMPLES | Lecture 19 of Course

D’Alembert’s Principle of Virtual Work | Active Forces & Workless Constraint Forces | Lecture 18

D’Alembert’s Principle of Virtual Work | Active Forces & Workless Constraint Forces | Lecture 18

Lagrange's Equations Intro, Generalized Coordinates, Constraints, Degrees of Freedom, Lecture 17

Lagrange's Equations Intro, Generalized Coordinates, Constraints, Degrees of Freedom, Lecture 17

Free Rigid Body Phase Space | Spin Stabilization of Frisbees (Flying Discs) | Lecture 16 of Course

Free Rigid Body Phase Space | Spin Stabilization of Frisbees (Flying Discs) | Lecture 16 of Course

Torque-Free Motion, Symmetric Rigid Body, Rigid Body Kinetic Energy, Caber Toss Analysis Lecture 15

Torque-Free Motion, Symmetric Rigid Body, Rigid Body Kinetic Energy, Caber Toss Analysis Lecture 15

Free Rigid Body Dynamics, Stability About Principal Axes, Spinning Qualitative Analysis | Lecture 14

Free Rigid Body Dynamics, Stability About Principal Axes, Spinning Qualitative Analysis | Lecture 14

Rigid Body Kinematic Differential Equation for Euler Angles & Rotation Matrix | Lecture 13 of Course

Rigid Body Kinematic Differential Equation for Euler Angles & Rotation Matrix | Lecture 13 of Course

Rotation Matrix, Euler Angles, Principal Axis-Angle of Rotation, 3D Rigid Body Kinematics Lecture 12

Rotation Matrix, Euler Angles, Principal Axis-Angle of Rotation, 3D Rigid Body Kinematics Lecture 12

Rotational Dynamics About Arbitrary Reference Point | Planar Rigid Body Motion, Car Jump, Lecture 11

Rotational Dynamics About Arbitrary Reference Point | Planar Rigid Body Motion, Car Jump, Lecture 11

Newton-Euler Equations for Rigid Body | Center of Mass & Inertia Tensor Worked Example | Lecture 10

Newton-Euler Equations for Rigid Body | Center of Mass & Inertia Tensor Worked Example | Lecture 10

Moment of Inertia Tensor/Matrix for a Rigid Body | Principal Axis Frame | Lecture 9 of Course

Moment of Inertia Tensor/Matrix for a Rigid Body | Principal Axis Frame | Lecture 9 of Course

Two Particle 2D Example, Energy Approach | Intro to Rigid Body of Particles & Kinematics | Lecture 8

Two Particle 2D Example, Energy Approach | Intro to Rigid Body of Particles & Kinematics | Lecture 8

Multi-Particle System: Center-of-Mass Frame, Angular Momentum, Energy & Applications | Lecture 7

Multi-Particle System: Center-of-Mass Frame, Angular Momentum, Energy & Applications | Lecture 7

Multi-Particle System, Center of Mass Motion, Total Linear Momentum, Superparticle Theorem Lecture 6

Multi-Particle System, Center of Mass Motion, Total Linear Momentum, Superparticle Theorem Lecture 6

Tetherball, Angular Momentum & Central Forces | Indiana Jones's Whip, Snake Tree Landing | Lecture 5

Tetherball, Angular Momentum & Central Forces | Indiana Jones's Whip, Snake Tree Landing | Lecture 5

Demonstrations of Transport Theorem for Kinematics | MATLAB for Mass Sliding on Parabola | Lecture 4

Demonstrations of Transport Theorem for Kinematics | MATLAB for Mass Sliding on Parabola | Lecture 4

Rotating & Translating Frames | Linear Momentum, Angular Momentum & Their Rates of Change, Lecture 3

Rotating & Translating Frames | Linear Momentum, Angular Momentum & Their Rates of Change, Lecture 3