> 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 --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://nkintc.gitbook.io/brainless/steam/engineering/machine-dynamics.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.