GLOSSARY.md

Glossary

Course contents · Method notes

Term	Meaning in this course	First useful lesson
State	Positions and velocities at one time	0
Integrator	A rule that approximates the next state from differential equations	1A
Step / timestep	One state update / its physical duration h	1A
Stage	An intermediate derivative or state estimate within one step	Methods
Output sample	A saved observation time; not necessarily every internal step	1C
Local error	Error introduced over one step, starting from the exact state in its theoretical definition	1B
Global error	Accumulated discrepancy at an observation time	1B
Order p	Exponent in resolved global error scaling approximately C h^p	1B
Tolerance	Scale controlling a local adaptive error decision, not a guaranteed final error	1C
Periapsis / apoapsis	Closest / farthest point of an elliptic two-body orbit	1C
Phase	Position along orbital motion; this course often uses unwrapped polar angle	1D
Invariant	A quantity conserved by the specified physical equations	1D
Symplectic	Preserving the canonical phase-space form; not synonymous with exact energy	Methods
Kepler subflow	Propagation of an isolated two-body component used inside a split method	1E
Jacobi coordinates	Each body's position relative to the center of mass of earlier bodies in the hierarchy	2A
Jerk	Time derivative of acceleration	Methods
Reference floor	Empirical scale below which the comparison does not resolve precise errors	2B
Reference horizon	Threshold- and sample-dependent end of usable pointwise reference agreement	2G
Restricted tracer	A particle that feels gravity without exerting backreaction	2R
Indirect acceleration	Correction for the acceleration of the translating heliocentric origin	2R
Jacobi integral	Conserved diagnostic of the circular restricted model in its rotating-frame formulation	2R
Softening	A declared modification of the short-distance gravitational law	3D
Half-mass radius	Center-of-mass radius containing at least half the mass	3D
Ensemble / seed	Multiple sampled initial systems / identifier controlling one initial realization	3E
Paired bootstrap	Resampling whole initial-condition seeds using matching draws for each method	3E
Total variation	Half the sum of absolute differences between histogram probability bins	3E
Regime	A model and objective under specified scales, duration, accuracy, and budget	3F
Pareto / non-dominated	No other candidate improves a listed cost component without worsening another, under the stated comparison	3F

Part 4 terms

Term	Meaning in this course	First useful lesson
Corrector / processed map	A canonical input/output transformation around an unchanged integration kernel; its label does not set the kernel's global order	4A
Mapping coordinates	The internal variables advanced by the split map, converted to physical coordinates for observations	4A
Conjugacy	A change of variables relating maps as P^-1 S P; chronological implementation order must match the formula	4A
Periapsis time t_p	The Kepler scale r_p/v_p, shorter than an orbital period for eccentric motion; h/t_p is a diagnostic, not a universal acceptance rule	4B
Hybrid / changeover	A scheme that changes the integration of selected Hamiltonian terms or regions near encounters; actual switches are distinct from distance proxies	4C
Objective ratio / margin	Measured objective divided by its positive target; fractional headroom is one minus that ratio, under the declared reference policy	4D
ZLK	von Zeipel–Lidov–Kozai exchange of eccentricity and relative inclination in a hierarchical system; simple peak formulas have limiting assumptions	4E
Secular observable	A declared slow or averaged diagnostic, such as an eccentricity peak or cycle period, checked separately from same-time trajectory accuracy	4E