Open Access
Table 1
List of symbols and notation.
| Symbol | Quantity |
|---|---|
| t | Time |
| dt | Time-step, small time interval |
| x, y, z | Cartesian coordinates |
| V | Volume |
| h = ∆a | Thickness of spherical shell |
 |
Position vector |
| r | Radial distance |
| υ = ṙ | Velocity vector |
| υ | Speed |
| d=r2−r1 | Difference position |
| d | Distance |
| u = υ2 − υ1 | Difference velocity |
| u | Relative speed |
| w = υ1 × υ2 | |
| G | Newton’s constant |
| M | Mass of central body |
| S | Radius of central body |
| m | Particle mass |
| s | Particle radius |
| t0 | Particle creation time |
| T | Orbit time |
| ω = 2π/T | Mean motion |
| Tcoll | Time between collisions |
| Tscat | Time between close encounters |
| Tprec | Precession period/time scale |
| Tsim | Total simulated time |
| a, b | Semimajor-, semiminor-axis |
| c = aϵ | Semi-focal separation |
| ℓ | Semi-latus rectum |
| r0 | Particle creation point |
| S | Spin angular momentum |
| L | Orbital angular momentum |
| K = L1 × L2 | Direction of nodal line |
| ϵ | Eccentricity vector |
| ϖ | Argument of periapsis |
| Ω | Ascending node |
| I | Inclination |
| v | True anomaly |
| E | Eccentric anomaly |
| ℛ | Rotation matrix |
| N | Number of particles |
| κ | Number of fragments |
| i, j | Particle indices |
| k, l | Rounds to collision |
| n | Counter |
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