Analytical Mechanics for Spacecraft Dynamics
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. The course starts by first developing D’Alembert’s principle and how the associated virtual work and virtual displacement concepts allows us to ignore non-working force terms.
Monthly Subscription Starting at AED 99 + VAT
- Level Expert
- المدة 32 ساعات hours
- الطبع بواسطة University of Colorado Boulder
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Offered by
عن
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. The course starts by first developing D’Alembert’s principle and how the associated virtual work and virtual displacement concepts allows us to ignore non-working force terms. Unconstrained systems and holonomic constrains are investigated. Next Kane's equations and the virtual power form of D'Alembert's equations are briefly reviewed for particles. Next Lagrange’s equations are developed which still assume a finite set of generalized coordinates, but can be applied to multiple rigid bodies as well. Lagrange multipliers are employed to apply Pfaffian constraints. Finally, Hamilton’s extended principle is developed to allow us to consider a dynamical system with flexible components. Here there are an infinite number of degrees of freedom. The course focuses on how to develop spacecraft related partial differential equations, but does not study numerically solving them. The course ends comparing the presented assumed mode methods to classical final element solutions.الوحدات
Introduction to Analytical Mechanics for Spacecraft Dynamics
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1
Videos
1
Videos
- Welcome to the Course!
Motivation for Analytical Mechanics
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1
Videos
1
Videos
- Motivation for Analytical Mechanics
D'Alembert's Principle
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14
Videos
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6
Assignment
6
Assignment
- Quiz 1 - Virtual Displacements
- Quiz 2 - Taking First Order Variations
- Quiz 3 - Virtual Work
- Quiz 4 - Classical Form of D'Alembert's Principle
- Quiz 5 - Virtual Power Form of D'Alembert's Equations
- Quiz 6 - Torques Acting on a Rigid Body
14
Videos
- 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
Constraints in Dynamical Systems
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5
Videos
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3
Assignment
3
Assignment
- Quiz 7 - Holonomic Constraints
- Quiz 8 - Multiple Constraints
- Quiz 9 - Pfaffian Constraints
5
Videos
- Holonomic Constraints
- Example: Spherical Pendulum
- Example: Constrained 3D Particle Motion
- Multiple Constraints
- Pfaffian Constraints
Constrained Optimization
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3
Videos
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1
Assignment
1
Assignment
- Quiz 10 - Constrained Optimization
3
Videos
- General Constrained Optimization
- Example: Extremum on Circles
- Discussion on Constrainted Optimization
Lagranian Dynamics
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15
Videos
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5
Assignment
5
Assignment
- Quiz 1 - Basic Lagrange's Equations
- Quiz 2 - Lagrange's Equations with Conservative Forces
- Quiz 3 - Constrained Lagrange's Equations
- Quiz 4 - Compact Matrix Form of Lagrange's Equations
- Quiz 5 - Cyclic Coordinates
15
Videos
- 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
Boltzmann Hamel Equations
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4
Videos
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1
Assignment
1
Assignment
- Quiz 1 - Boltzmann Hamel Equations
4
Videos
- Motivation for Boltzmann Hamel Equations
- Quasi Velocity Coordinates
- Boltzmann Hamel Equation Development
- Example: Rigid Body Motion in Free Space
Hamilton's Principles
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9
Videos
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3
Assignment
3
Assignment
- Quiz 1 - Variational Calculus
- Quiz 2 - Hamilton's Principles
- Quiz 3 - Hamilton's Law of Varying Action
9
Videos
- 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
Hamilton's Principle on a Continuous System
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3
Videos
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1
Assignment
1
Assignment
- Quiz 4 - Non-Uniform Axially Elastic Rod
3
Videos
- Review of Hamilton's Extended Principle
- Non-Uniform Axially Elastic Rod
- Example: Elastic Rod with External Force
Hybrid Dynamical Systems
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5
Videos
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1
Assignment
1
Assignment
- Quiz 5 - Hybrid Dynamical Systems
5
Videos
- Motivation for Hybrid Systems
- Hybrid Coordinate Definitions
- Hybrid Lagrangian Formulation
- Example: Axial Rod and Spring-Mass System
- Example: Hub with Euler-Bernoulli Beam
Finite Dimensional Modeling of Continuous Systems
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4
Videos
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2
Assignment
2
Assignment
- Quiz 6 - Finite Dimensional Modeling
- Quiz 7 - Input Shaped Attitude Control
4
Videos
- Motivation for Reduction to a Finite Set of Coordinates
- Assumed Modes Method
- Example
- Input Shaped Attitude Control
Auto Summary
Dive deep into the world of spacecraft dynamics with "Analytical Mechanics for Spacecraft Dynamics," a specialized course within the Advanced Spacecraft Dynamics and Control series. Designed for those with a solid grounding in spacecraft dynamics, this course delves into analytical mechanics methodologies to efficiently develop motion equations. Explore advanced concepts starting with D’Alembert’s principle, virtual work, and virtual displacement, moving through unconstrained systems and holonomic constraints. Gain insights into Kane's equations and the virtual power form, and master Lagrange’s equations for both finite generalized coordinates and multiple rigid bodies, utilizing Lagrange multipliers for Pfaffian constraints. Progress to Hamilton’s extended principle, addressing systems with flexible components and infinite degrees of freedom, and learn to formulate spacecraft-related partial differential equations. The course culminates in a comparison of assumed mode methods with traditional finite element solutions. Led by Coursera, this expert-level course spans approximately 1920 minutes and is available under the Starter subscription plan. Ideal for advanced learners in the science and engineering domain, it provides the analytical tools necessary for mastering spacecraft dynamics and control.
Hanspeter Schaub