## Class PVCoordinates

• ### Field Detail

• #### ZERO

public static final PVCoordinates ZERO
Fixed position/velocity at origin (both p, v and a are zero vectors).
• ### Constructor Detail

• #### PVCoordinates

public PVCoordinates()
Simple constructor.

Set the Coordinates to default : (0 0 0), (0 0 0), (0 0 0).

• #### PVCoordinates

public PVCoordinates​(Vector3D position,
Vector3D velocity)
Builds a PVCoordinates triplet with zero acceleration.

Acceleration is set to zero

Parameters:
position - the position vector (m)
velocity - the velocity vector (m/s)
• #### PVCoordinates

public PVCoordinates​(Vector3D position,
Vector3D velocity,
Vector3D acceleration)
Builds a PVCoordinates triplet.
Parameters:
position - the position vector (m)
velocity - the velocity vector (m/s)
acceleration - the acceleration vector (m/s²)
• #### PVCoordinates

public PVCoordinates​(double a,
PVCoordinates pv)
Multiplicative constructor.

Build a PVCoordinates from another one and a scale factor.

The PVCoordinates built will be a * pv

Parameters:
a - scale factor
pv - base (unscaled) PVCoordinates
• #### PVCoordinates

public PVCoordinates​(PVCoordinates start,
PVCoordinates end)
Subtractive constructor.

Build a relative PVCoordinates from a start and an end position.

The PVCoordinates built will be end - start.

Parameters:
start - Starting PVCoordinates
end - ending PVCoordinates
• #### PVCoordinates

public PVCoordinates​(double a1,
PVCoordinates pv1,
double a2,
PVCoordinates pv2)
Linear constructor.

Build a PVCoordinates from two other ones and corresponding scale factors.

The PVCoordinates built will be a1 * u1 + a2 * u2

Parameters:
a1 - first scale factor
pv1 - first base (unscaled) PVCoordinates
a2 - second scale factor
pv2 - second base (unscaled) PVCoordinates
• #### PVCoordinates

public PVCoordinates​(double a1,
PVCoordinates pv1,
double a2,
PVCoordinates pv2,
double a3,
PVCoordinates pv3)
Linear constructor.

Build a PVCoordinates from three other ones and corresponding scale factors.

The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3

Parameters:
a1 - first scale factor
pv1 - first base (unscaled) PVCoordinates
a2 - second scale factor
pv2 - second base (unscaled) PVCoordinates
a3 - third scale factor
pv3 - third base (unscaled) PVCoordinates
• #### PVCoordinates

public PVCoordinates​(double a1,
PVCoordinates pv1,
double a2,
PVCoordinates pv2,
double a3,
PVCoordinates pv3,
double a4,
PVCoordinates pv4)
Linear constructor.

Build a PVCoordinates from four other ones and corresponding scale factors.

The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4

Parameters:
a1 - first scale factor
pv1 - first base (unscaled) PVCoordinates
a2 - second scale factor
pv2 - second base (unscaled) PVCoordinates
a3 - third scale factor
pv3 - third base (unscaled) PVCoordinates
a4 - fourth scale factor
pv4 - fourth base (unscaled) PVCoordinates
• #### PVCoordinates

public PVCoordinates​(FieldVector3D<U> p)
Builds a PVCoordinates triplet from a FieldVector3D<Derivative>.

The vector components must have time as their only derivation parameter and have consistent derivation orders.

Type Parameters:
U - type of the derivative
Parameters:
p - vector with time-derivatives embedded within the coordinates
• #### PVCoordinates

public PVCoordinates​(Vector3D position)
Builds PV coordinates with the givne position, zero velocity, and zero acceleration.
Parameters:
position - position vector (m)
• ### Method Detail

• #### toDerivativeStructureVector

public FieldVector3D<DerivativeStructure> toDerivativeStructureVector​(int order)
Transform the instance to a FieldVector3D<DerivativeStructure>.

The DerivativeStructure coordinates correspond to time-derivatives up to the user-specified order.

Parameters:
order - derivation order for the vector components (must be either 0, 1 or 2)
Returns:
vector with time-derivatives embedded within the coordinates
• #### toDerivativeStructurePV

public FieldPVCoordinates<DerivativeStructure> toDerivativeStructurePV​(int order)
Transform the instance to a FieldPVCoordinates<DerivativeStructure>.

The DerivativeStructure coordinates correspond to time-derivatives up to the user-specified order. As both the instance components position, velocity and acceleration and the derivatives of the components holds time-derivatives, there are several ways to retrieve these derivatives. If for example the order is set to 2, then both pv.getPosition().getX().getPartialDerivative(2), pv.getVelocity().getX().getPartialDerivative(1) and pv.getAcceleration().getX().getValue() return the exact same value.

If derivation order is 1, the first derivative of acceleration will be computed as a Keplerian-only jerk. If derivation order is 2, the second derivative of velocity (which is also the first derivative of acceleration) will be computed as a Keplerian-only jerk, and the second derivative of acceleration will be computed as a Keplerian-only jounce.

Parameters:
order - derivation order for the vector components (must be either 0, 1 or 2)
Returns:
pv coordinates with time-derivatives embedded within the coordinates
Since:
9.2
• #### toUnivariateDerivative2PV

public FieldPVCoordinates<UnivariateDerivative2> toUnivariateDerivative2PV()
Transform the instance to a FieldPVCoordinates<UnivariateDerivative2>.

The UnivariateDerivative2 coordinates correspond to time-derivatives up to the order 2. As derivation order is 2, the second derivative of velocity (which is also the first derivative of acceleration) will be computed as a Keplerian-only jerk, and the second derivative of acceleration will be computed as a Keplerian-only jounce.

Returns:
pv coordinates with time-derivatives embedded within the coordinates
Since:
10.2
• #### estimateVelocity

public static Vector3D estimateVelocity​(Vector3D start,
Vector3D end,
double dt)
Estimate velocity between two positions.

Estimation is based on a simple fixed velocity translation during the time interval between the two positions.

Parameters:
start - start position
end - end position
dt - time elapsed between the dates of the two positions
Returns:
velocity allowing to go from start to end positions
• #### shiftedBy

public PVCoordinates shiftedBy​(double dt)
Get a time-shifted state.

The state can be slightly shifted to close dates. This shift is based on a simple Taylor expansion. It is not intended as a replacement for proper orbit propagation (it is not even Keplerian!) but should be sufficient for either small time shifts or coarse accuracy.

Specified by:
shiftedBy in interface TimeShiftable<PVCoordinates>
Parameters:
dt - time shift in seconds
Returns:
a new state, shifted with respect to the instance (which is immutable)
• #### positionShiftedBy

public Vector3D positionShiftedBy​(double dt)
Get a time-shifted position. Same as shiftedBy(double) except that only the sifted position is returned.

The state can be slightly shifted to close dates. This shift is based on a simple Taylor expansion. It is not intended as a replacement for proper orbit propagation (it is not even Keplerian!) but should be sufficient for either small time shifts or coarse accuracy.

Parameters:
dt - time shift in seconds
Returns:
a new state, shifted with respect to the instance (which is immutable)
• #### getPosition

public Vector3D getPosition()
Gets the position.
Returns:
the position vector (m).
• #### getVelocity

public Vector3D getVelocity()
Gets the velocity.
Returns:
the velocity vector (m/s).
• #### getAcceleration

public Vector3D getAcceleration()
Gets the acceleration.
Returns:
the acceleration vector (m/s²).
• #### getMomentum

public Vector3D getMomentum()
Gets the momentum.

This vector is the p ⊗ v where p is position, v is velocity and ⊗ is cross product. To get the real physical angular momentum you need to multiply this vector by the mass.

The returned vector is recomputed each time this method is called, it is not cached.

Returns:
a new instance of the momentum vector (m²/s).
• #### getAngularVelocity

public Vector3D getAngularVelocity()
Get the angular velocity (spin) of this point as seen from the origin.

The angular velocity vector is parallel to the angular momentum and is computed by ω = p × v / ||p||²

Returns:
the angular velocity vector
Angular Velocity on Wikipedia
• #### negate

public PVCoordinates negate()
Get the opposite of the instance.
Returns:
a new position-velocity which is opposite to the instance
• #### normalize

public PVCoordinates normalize()
Normalize the position part of the instance.

The computed coordinates first component (position) will be a normalized vector, the second component (velocity) will be the derivative of the first component (hence it will generally not be normalized), and the third component (acceleration) will be the derivative of the second component (hence it will generally not be normalized).

Returns:
a new instance, with first component normalized and remaining component computed to have consistent derivatives
• #### crossProduct

public static PVCoordinates crossProduct​(PVCoordinates pv1,
PVCoordinates pv2)
Compute the cross-product of two instances.
Parameters:
pv1 - first instances
pv2 - second instances
Returns:
the cross product v1 ^ v2 as a new instance
• #### toString

public String toString()
Return a string representation of this position/velocity pair.
Overrides:
toString in class Object
Returns:
string representation of this position/velocity pair