AER506 Spacecraft Dynamics and Control I — Course Notes (Kinematics)
Author: C. J. Damaren · Year: 2003 (PDF creation metadata) · Venue: unpublished course notes, University of Toronto, 13 pp. Raw: md · pdf
Summary
The kinematics chapter of Damaren’s U of T spacecraft dynamics course: vectrix resolution of physical vectors ( as a column of basis vectors, explicitly named a vectrix), dot/cross products in component form and the skew-symmetric matrix, rotation matrices between frames, principal rotations, angular velocity (including from a given ), Euler angles with the 3-2-1 sequence, infinitesimal rotations, Euler parameters via Euler’s theorem, and attitude solution given angular velocity. The corpus copy is a LightOnOCR conversion of an image scan: 11/13 pages fp16 (pc2), pages 10-11 redone bf16 on the workstation, 13/13 zero-degeneracy.
Key Claims
- Same kinematic substrate as deruiter2021attitude, independently authored — rotation matrix, principal rotations, Euler’s theorem, Euler parameters — useful as a cross-check text, not new theory.
- Second independent provenance anchor for “vectrix”: the notes define the term explicitly (“We shall refer to as a vectrix”), strengthening the terminology case beyond the de Ruiter notes (feeds the vectrix research card).
- Orbital (translational) and attitude (rotational) motion are treated as uncoupled for a rigid spacecraft — the classical simplification our free-flying manipulator regime explicitly breaks.
Method
Vectrix/component matrix algebra throughout, same lineage as the de Ruiter notes (U of T school); worked derivations, no Lie-group formalism.
Regime note. Rigid single spacecraft, no manipulator; the orbital/attitude decoupling claim does not carry to the coupled FFSM regime.
Relevance to thesis
Peripheral: content overlaps deruiter2021attitude, which remains the recon’s substrate document. Value is corroborative — an independent statement of the same identities for cross-checking theorem statements, and the second citable definition of vectrix notation.
Connections
Topics: Unit Quaternion (Euler parameters) Sources: deruiter2021attitude (same substrate, richer identity machinery) · deruiter2014general (the published identity proofs)
Open Questions
- OCR fidelity spot-audit: sample 2 display equations (one from the bf16-redone pages 10-11) against the scan before quoting.