Analytical Mechanics (course notes)
Author: Anton H. J. de Ruiter · Year: 2022 (compile) · Venue: unpublished course notes, 34 pp. — part 2 of the numbered series (part 1 = deruiter2021attitude); authorship confirmed by the note owner 2026-07-09 Raw: md · pdf
Summary
Energy-based mechanics from first principles, complementing Newton’s force-based formulation: generalized coordinates, Lagrange’s equations, holonomic vs non-holonomic constraints ( vs ), constraint forces and the principle of virtual work, finite-sized bodies, Hamilton’s extended principle, modelling of flexible spacecraft, and Hamilton’s equations. The corpus copy is a LightOnOCR conversion of an image scan (no text layer): 34/34 pages, zero degeneracy, equations render as tagged LaTeX.
Key Claims
- Holonomic constraints differentiate into the non-holonomic (Pfaffian) form, so both are treated uniformly at velocity level — the same constraint shape the manipulator’s differential kinematics uses.
- Lagrange’s equations derived for generalized coordinates with constraint forces eliminated via virtual work.
- Hamilton’s extended principle covers the flexible-spacecraft case — the notes’ bridge from rigid-body dynamics to distributed-parameter models.
Method
Same direct style as the series: gradients/Jacobians per the shared Preliminaries section, matrix calculus throughout, worked examples per major section.
Regime note. Generic mechanics; the flexible-spacecraft section is spacecraft-specific but regime-agnostic (no manipulator).
Relevance to thesis
The Lagrangian substrate under the manipulator equations of motion (the circumcentroidal block is born of exactly this machinery). Candidate source for the theorem recon’s dynamics rungs once the SO(3)/attitude arc clears — Lagrange-equation derivations are further from Mathlib’s current shoreline than the matrix identities of part 1, so this file feeds later rungs.
Connections
Topics: FFSM Dynamics Sources: deruiter2021attitude · slotine1991applied (its Ch. 9 multi-input physical systems consume the same Lagrangian structure)
Open Questions
- OCR fidelity spot-audit: sample 3 display equations against the scan before any theorem statement is quoted from this md (OCR, not text-layer — one grade below the part-1 transcription).