Ementorhub

What you'll learn

Use virtual work methods to develop equations of motion of mechanical systems.

Understand how to use Lagrange multipliers to study constrained dynamical systems.

Be able to derive the equations of motion of a spacecraft with flexible sub-components.

Skills you'll gain

Finite Element Methods

Engineering Analysis

Differential Equations

Applied Mathematics

Mechanics

Calculus

Vibrations

Mathematical Modeling

Linear Algebra

There are 3 modules in this course

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. The material covered is taking from the book "Analytical Mechanics of Space Systems" available at https://arc.aiaa.org/doi/book/10.2514/4.105210.

Energy Based Equations of Motion

Variational Methods in Analytical Dynamics