ProtoFlux:TrajectoryPosition

Trajectory Position

Initial Velocity

*

Gravity

Drag

Time

Physics

The Trajectory Position node takes an initial velocity, force of gravity, drag, and time period, and then outputs the change in position of an object that it would experience. This is very useful for simulating movement.

Its formula is derived from objects moving at low speed / through thick fluids where they experience drag that grows linearly with velocity. (Trajectory of a Projectile with Stokes Drag)

It runs a division by drag (squared). This will result in an invalid value when drag is zero and reduced accuracy for values close to zero.

Inputs

Initial Velocity (float3)

The initial velocity (speed and direction).

Gravity (float3)

The direction and strength of gravity.

Drag (float)

The resistance in movement. (positive value, not too close to 0 to avoid inaccurate results)

Time (float)

The change in time between initial and final position.

Outputs

* (float3)

The change in position that would have happened in the time frame. It is computed using the following formula:

$T r a j e c t o r y P o s i t i o n (T i m e) = \frac{e^{- D r a g * T i m e} * (e^{D r a g * T i m e} * (G r a v i t y * D r a g * T i m e + D r a g * I n i t i a l V e l o c i t y - G r a v i t y) - D r a g * I n i t i a l V e l o c i t y + G r a v i t y)}{D r a g^{2}}$

Examples

No examples have been given at this time. Examples of potential uses include:

Instantly calculating the end position of a projectile
Simulating the movement of a ball