Special purpose integrator for precise integration of the three body problem. More...

Inheritance diagram for AZTripleIntegrator:

Public Member Functions
void	Setup (int maxBodies, double timeStep)
	Setup the specified maxBodies and timeStep. Must be called prior to PreEvolve/Evolve.

void	Clear ()
	Clear internal information so no bodies are evolved.

INBodyIntegrator	DeepClone ()
	Clone this instance, replicating internal arrays. Copy across any internal state required for continued evolution.

void	AddNBody (int bodyNum, NBody nbody, GravityState.NbodyState[] nbodyStates)
	Adds the N body. Implementation may support the case where the initial number of bodies in Setup() is exceeded, creating space, or may ignore additions that exceed this limit (e.g. AZTTriple).

void	RemoveBodyAtIndex (int atIndex)
	Removes NBody at index i.

void	GrowArrays (int growBy)
	Grows the arrays. Called by GravityEngine when it changes internal data sizes.

Vector3	GetVelocityForIndex (int i)

void	GetVelocityDoubleForIndex (int i, ref double[] vel)

void	SetVelocityForIndex (int i, Vector3 vel)

void	SetVelocityDoubleForIndex (int i, ref double[] v)

Vector3d	GetAccelerationForIndex (int i)

float	GetEnergy (GravityState gravityState)
	Gets the energy of the system.

float	GetInitialEnergy (GravityState gravityState)
	Gets the initial energy.

void	PreEvolve (GravityState gravityState)
	Call ONCE after all game objects have been added to allow integrator to pre-calc starting quantities required for integration.

double	Evolve (double evolveTime, GravityState gravityState, bool exactTime=false)
	Evolve the specified evolveTime, m_arg and r_arg.

void	SetPositionDoubleForIndex (int i, ref double[] v)

string	GetExternalAccelForIndex (int i)

void	Setup (int maxBodies, double timeStep)
	Setup the specified maxBodies and timeStep. Must be called prior to PreEvolve/Evolve.

void	Clear ()
	Clear internal information so no bodies are evolved.

INBodyIntegrator	DeepClone ()
	Clone this instance, replicating internal arrays. Copy across any internal state required for continued evolution.

void	AddNBody (int bodyNum, NBody nbody, GravityState.NbodyState[] nbodyState)
	Adds the N body. Implementation may support the case where the initial number of bodies in Setup() is exceeded, creating space, or may ignore additions that exceed this limit (e.g. AZTTriple).

void	RemoveBodyAtIndex (int atIndex)
	Removes NBody at index i.

void	GrowArrays (int growBy)
	Grows the arrays. Called by GravityEngine when it changes internal data sizes.

Vector3d	GetAccelerationForIndex (int i)

string	GetExternalAccelForIndex (int i)

void	PreEvolve (GravityState gravityState)
	Call ONCE after all game objects have been added to allow integrator to pre-calc starting quantities required for integration.

double	Evolve (double time, GravityState gravityState, bool exactTime=false)
	Evolve the specified time, m, r and info.

float	GetEnergy (GravityState gs)
	Gets the energy of the system.

float	GetInitialEnergy (GravityState gs)
	Gets the initial energy.

Detailed Description

Special purpose integrator for precise integration of the three body problem.

The code derives from Fortran code written by Sevre Aarseth in the 1970s.

The key algorithm detail is the use of mathematical regularization to handle close encounters where the use of 1/r^2 would result in numerical instability. The "trick" is to use a change of variables to u=1/r for the two interacting bodies.

The integrator has been extended to handle additional bodies by using Leapfrog to evolve the additional bodies subject to the gravity of the AZT controlled bodies. Adding more than three massive bodies will result in inaccurate modelling, since first three bodies added will not be affected by the fourth.

Member Function Documentation

◆ AddNBody()

void AZTripleIntegrator.AddNBody	(	int	bodyNum,
		NBody	nbody,
		GravityState.NbodyState[]	nbodyState
	)

Adds the N body. Implementation may support the case where the initial number of bodies in Setup() is exceeded, creating space, or may ignore additions that exceed this limit (e.g. AZTTriple).

Parameters

nbody NBody component

Implements INBodyIntegrator.

◆ Clear()

void AZTripleIntegrator.Clear ( )

Clear internal information so no bodies are evolved.

Implements INBodyIntegrator.

◆ DeepClone()

INBodyIntegrator AZTripleIntegrator.DeepClone ( )

Clone this instance, replicating internal arrays. Copy across any internal state required for continued evolution.

Implements INBodyIntegrator.

◆ Evolve()

double AZTripleIntegrator.Evolve	(	double	evolveTime,
		GravityState	gravityState,
		bool	exactTime = `false`
	)

Evolve the specified evolveTime, m_arg and r_arg.

AZT is focused on accuracy and the time it evolves for can vary over several orders of magnitude.

Parameters

evolveTime	Evolve time.
m_arg	M_arg. NOT USED
r_arg	R_arg. passes results back

Implements INBodyIntegrator.

◆ GetAccelerationForIndex()

Vector3d AZTripleIntegrator.GetAccelerationForIndex ( int i )

Implements INBodyIntegrator.

◆ GetEnergy()

float AZTripleIntegrator.GetEnergy ( GravityState gs )

Gets the energy of the system.

Returns: The energy.

Parameters

mass	Mass.
pos	Position.

Implements INBodyIntegrator.

◆ GetExternalAccelForIndex()

string AZTripleIntegrator.GetExternalAccelForIndex ( int i )

Implements INBodyIntegrator.

◆ GetInitialEnergy()

float AZTripleIntegrator.GetInitialEnergy ( GravityState gs )

Gets the initial energy.

Returns: The initial energy.

Parameters

mass	Mass.
pos	Position.

Implements INBodyIntegrator.

◆ GrowArrays()

void AZTripleIntegrator.GrowArrays ( int growBy )

Grows the arrays. Called by GravityEngine when it changes internal data sizes.

Parameters

growBy Grow by.

Implements INBodyIntegrator.

◆ PreEvolve()

void AZTripleIntegrator.PreEvolve ( GravityState gravityState )

Call ONCE after all game objects have been added to allow integrator to pre-calc starting quantities required for integration.

To avoid copies of mass and position arrays in integrators provide a reference to these for Evolve and PreEvolve

Some implementations (e.g. AZTriple) may make their own copies and then copy the result back into these arrays ///

Parameters

m	M.
r	The red component.
info	Info.

Implements INBodyIntegrator.

◆ RemoveBodyAtIndex()

void AZTripleIntegrator.RemoveBodyAtIndex ( int atIndex )

Removes NBody at index i.

Parameters

atIndex At index.

Implements INBodyIntegrator.

◆ Setup()

void AZTripleIntegrator.Setup	(	int	maxBodies,
		double	timeStep
	)

Setup the specified maxBodies and timeStep. Must be called prior to PreEvolve/Evolve.

Parameters

maxBodies	Max bodies.
timeStep	Time step.

Implements INBodyIntegrator.

The documentation for this class was generated from the following file:

C:/Users/musgr/Documents/Unity/gravityengine/Assets/GravityEngine/Scripts/Engine/Integrators/AZTripleIntegrator.cs

Public Member Functions

Detailed Description

Member Function Documentation

◆ AddNBody()

◆ Clear()

◆ DeepClone()

◆ Evolve()

◆ GetAccelerationForIndex()

◆ GetEnergy()

◆ GetExternalAccelForIndex()

◆ GetInitialEnergy()

◆ GrowArrays()

◆ PreEvolve()

◆ RemoveBodyAtIndex()

◆ Setup()