Notation Quick-Reference Card
reference
A printable one-page summary of the control-affine terms and physical symbols; the full Notation Reference has definitions and sign conventions.
NoteHow to Use This Card
This is a condensed lookup card, not the normative source. Every entry below is defined in full — with derivations, qualifiers, and sign conventions — in the Mathematical Notation Reference, which remains authoritative. Print this page (browser Print, Letter or A4) for a one-page reference while reading the textbook series.
Control-Affine Form
\[\dot{x} = f(x) + G(x)u\]
| Symbol | Meaning |
|---|---|
| \(x\) | Modeled state |
| \(f(x)\) | Drift: autonomous evolution at zero declared control |
| \(G(x)u\) | Declared control-input contribution |
Canonical Acronyms
| Acronym | Expansion |
|---|---|
| ZTCF (family) | Zero-Torque Counterfactual |
| ZVCF | Zero-Velocity Counterfactual |
| DCR | Drift-Control Ratio |
| DgCR | Drag-Curve Ratio |
Core Physical Quantities
| Symbol | Quantity | Units |
|---|---|---|
| \(r\), \(x\) | Position | m |
| \(v\) | Velocity | m/s |
| \(a\) | Acceleration | m/s² |
| \(\omega\) | Angular velocity | rad/s |
| \(\alpha\) | Angular acceleration | rad/s² |
| \(m\) | Mass | kg |
| \(F\) | Force | N |
| \(\tau\) | Torque | N·m |
| \(I\) | Moment of inertia | kg·m² |
| \(p\) | Linear momentum | kg·m/s |
| \(L\) | Angular momentum | kg·m²/s |
Axis Convention
Right-handed frame, \(z = x \times y\): X forward/longitudinal (roll), Y lateral (pitch), Z vertical/up (yaw).
Citation
BibTeX citation: Download .bib
@online{untitled,
author = {},
title = {Notation {Quick-Reference} {Card}},
url = {https://affinedrift.com/pages/notation-quick-reference.html},
langid = {en}
}
For attribution, please cite this work as:
“Notation Quick-Reference Card.” n.d. https://affinedrift.com/pages/notation-quick-reference.html.