University of Colorado Boulder - Analytical Mechanics for Spacecraft Dynamics
- Offered byCoursera
Analytical Mechanics for Spacecraft Dynamics at Coursera Overview
Duration | 32 hours |
Total fee | Free |
Mode of learning | Online |
Official Website | Explore Free Course  |
Credential | Certificate |
Analytical Mechanics for Spacecraft Dynamics at Coursera Highlights
- Earn a Certificate upon completion from University of Colorado Boulder
Analytical Mechanics for Spacecraft Dynamics at Coursera Course details
- This course is part 2 of the specialization Advanced Spacecraft Dynamics and Control
- It assumes you have a strong foundation in spacecraft dynamics and control, including particle dynamics, rotating frame, rigid body kinematics and kinetics
- The focus of the course is to understand key analytical mechanics methodologies to develop equations of motion in an algebraically efficient manner
Analytical Mechanics for Spacecraft Dynamics at Coursera Curriculum
Generalized Methods of Analytical Mechanics
Welcome to the Course!
Motivation for Analytical Mechanics
Introduction
Virtual Displacements
Taking First Order Variations
Virtual Work
Example: Circularly Orbiting Particle
Example: Planar Spinning Body
Classical Form of D'Alembert's Principle
Example: Falling Rod Revisited
Example: Generalized Forces on Particle
Virtual Power Form of D'Alembert's Equations
Example: Cart-Pendulum System
Example: Planar Orbital Motion
Torques Acting on a Rigid Body
Example: Generalized Force on 2-Link System
Holonomic Constraints
Example: Spherical Pendulum
Example: Constrained 3D Particle Motion
Multiple Constraints
Pfaffian Constraints
General Constrained Optimization
Example: Extremum on Circles
Discussion on Constrainted Optimization
Virtual Displacements
Taking First Order Variations
Virtual Work
Classical Form of D'Alembert's Principle
Virtual Power Form of D'Alembert's Equations
Torques Acting on a Rigid Body
Holonomic Constraints
Multiple Constraints
Pfaffian Constraints
Constrained Optimization
Energy Based Equations of Motion
Derivation of Basic Lagrange's Equations
Review: Lagrangian Dynamics
Example: Particle in a Plane
Lagrange's Equations with Conservative Forces
Example: Cart-Pendulum revisited with Lagrange's equationsrev
Constrained Lagrange's Equations
Example: Particle in Rotating Tube
Example: Rolling Wheel
Example: Falling Ring
Compact Matrix Form of Lagrange's Equations
Cyclic Coordinates
Example: Falling Planar Particle
Example: Planar Particle on a Spring
Routhian Reduction
Example: Falling Planar Particle With Routhian
Motivation for Boltzmann Hamel Equations
Quasi Velocity Coordinates
Boltzmann Hamel Equation Development
Example: Rigid Body Motion in Free Space
Basic Lagrange's Equations
Lagrange's Equations with Conservative Forces
Constrained Lagrange's Equations
Compact Matrix Form of Lagrange's Equations
Cyclic Coordinates
Boltzmann Hamel Equations
Variational Methods in Analytical Dynamics
Motivation for Variational Methods
Variational Calculus
Hamilton's Principle Function
Hamilton's Variational Principles
Example: Spring-Mass-Damper System
Extremun of Hamilton's Principle Function
Hamilton's Law of Varying Action
Example: Particle In Gravity Field
Example: Linear Oscillator System
Review of Hamilton's Extended Principle
Non-Uniform Axially Elastic Rod
Example: Elastic Rod with External Force
Motivation for Hybrid Systems
Hybrid Coordinate Definitions
Hybrid Lagrangian Formulation
Example: Axial Rod and Spring-Mass System
Example: Hub with Euler-Bernoulli Beam
Motivation for Reduction to a Finite Set of Coordinates
Assumed Modes Method
Example
Input Shaped Attitude Control
Variational Calculus
Hamilton's Principles
Hamilton's Law of Varying Action
Non-Uniform Axially Elastic Rod
Hybrid Dynamical Systems
Finite Dimensional Modeling
Input Shaped Attitude Control
Other courses offered by Coursera
Student Forum
Anything you would want to ask experts?