Proving the Cross Product Rules with the Levi-Civita Symbol

Downloadable Files

• Derivation sheet.md
• Code Snippets.rar
• Code Snippets with Diagrams.md

Summary

These files provide a comprehensive technical and visual bridge between abstract tensor algebra and 3D rotational mechanics. The material begins by using the Levi-Civita symbol to prove the fundamental cross-product rules of basis vectors, establishing the "algebraic engine" required for advanced physics. This mathematical foundation is then applied to real-world mechanical concepts—such as Torque, Angular Momentum, and the Inertia Tensor—through five detailed Python-based animations that visualize how mass distribution and vector coupling influence rotational stability and the "wobbling" effect in rigid bodies. To ensure technical clarity, the collection includes extensive Mermaid diagrams that map the logical flow from symbolic code execution to the geometric synthesis of the Inertia Ellipsoid.

Kanban

Kanban: Rotational Formalism: Tensor Mechanics and Index Identities