> For the complete documentation index, see [llms.txt](https://nkintc.gitbook.io/brainless/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nkintc.gitbook.io/brainless/steam/engineering/machine-dynamics.md).

# Machine Dynamics

Lecture 1: Introduction

Lecture 2: Vector Reference Frame

Lecture 3: Basis Transformation

Lecture 4: Space vs Body Rotation

Lecture 5: Cross Product Matrix

Lecture 6: Analytic Derivative

Lecture 7: Kinematic Derivative and Angular Velocity

Lecture 8: Velocity and Acceleration Equations

Lecture 9: Recursive Equation

Lecture 10: Acceleration Equation from Midpoint

Lecture 11: Motion Genesis

Lecture 12: Constrained Equation due to Rolling Path Variable

Lecture 13: Rolling Constant 

Lecture 14: Path Variable

Lecture 15: Constrained Path Example 

Lecture 16: Mass Distribution

Lecture 17: Inertial Properties

Lecture 18: Newton-Euler Equations

Lecture 19: Newton-Euler Equations on A Rotating Plate ODE