Subsection 1.8 · Kinematics model for gaming
Vector Run
Aim your launch, fly into the ring — and arrive slower than the docking limit.
Thrust changes velocity, not position. Velocity keeps going on its own.
Hold a direction to build speed, then hold the opposite one to lose it.
W A S D thrust · Enter launches · R re-aims
- Simple definition
- A kinematics game model adds acceleration to velocity, then velocity to position, once every small time step.
- Example
- Holding a thrust key raises the velocity every frame, so the craft keeps moving after you let go.
How the physics works
The simulator advances 120 times a second. Each step reads your thrust direction, adds the level’s field, and applies two lines of semi-implicit Euler integration:
- a = athrust + afield
- v ← v + a Δt
- r ← r + v Δt
The gold dashed line while you aim runs exactly those two lines forward with the thrust switched off, so it is a true preview of your launch: watch it bend as the field acts on it. Because position is only ever changed by velocity, a key press can never move the craft directly — it can only change how fast the craft is already going. That is why you have to brake early.
Docking compares your velocity with the ring’s velocity, not with the ground. The four levels change only the field term: nothing, a moving medium (a = k(vflow − v)), a constant g, and an inverse-square pull (a = μ/r²) toward a planet.