## Class FieldPVCoordinates<T extends CalculusFieldElement<T>>

• Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
FieldBlendable<FieldPVCoordinates<T>,​T>, FieldTimeShiftable<FieldPVCoordinates<T>,​T>, TimeShiftable<FieldPVCoordinates<T>>
Direct Known Subclasses:
TimeStampedFieldPVCoordinates

public class FieldPVCoordinates<T extends CalculusFieldElement<T>>
extends Object
implements FieldTimeShiftable<FieldPVCoordinates<T>,​T>, FieldBlendable<FieldPVCoordinates<T>,​T>
Simple container for Position/Velocity pairs, using CalculusFieldElement.

The state can be slightly shifted to close dates. This shift is based on a simple linear model. 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.

This class is the angular counterpart to FieldAngularCoordinates.

Instances of this class are guaranteed to be immutable.

Since:
6.0
Author:
Luc Maisonobe
PVCoordinates
• ### Constructor Summary

Constructors
Constructor Description
FieldPVCoordinates​(double a, FieldPVCoordinates<T> pv)
Multiplicative constructor.
FieldPVCoordinates​(double a1, FieldPVCoordinates<T> pv1, double a2, FieldPVCoordinates<T> pv2)
Linear constructor.
FieldPVCoordinates​(double a1, FieldPVCoordinates<T> pv1, double a2, FieldPVCoordinates<T> pv2, double a3, FieldPVCoordinates<T> pv3)
Linear constructor.
FieldPVCoordinates​(double a1, FieldPVCoordinates<T> pv1, double a2, FieldPVCoordinates<T> pv2, double a3, FieldPVCoordinates<T> pv3, double a4, FieldPVCoordinates<T> pv4)
Linear constructor.
FieldPVCoordinates​(Field<T> field, PVCoordinates pv)
Builds a FieldPVCoordinates from a field and a regular PVCoordinates.
FieldPVCoordinates​(FieldVector3D<T> position, FieldVector3D<T> velocity)
Builds a FieldPVCoordinates triplet with zero acceleration.
FieldPVCoordinates​(FieldVector3D<T> position, FieldVector3D<T> velocity, FieldVector3D<T> acceleration)
Builds a FieldPVCoordinates triplet.
FieldPVCoordinates​(FieldVector3D<U> p)
Builds a FieldPVCoordinates triplet from a FieldVector3D<FieldDerivativeStructure>.
FieldPVCoordinates​(FieldPVCoordinates<T> start, FieldPVCoordinates<T> end)
Subtractive constructor.
FieldPVCoordinates​(T a, FieldPVCoordinates<T> pv)
Multiplicative constructor.
FieldPVCoordinates​(T a1, FieldPVCoordinates<T> pv1, T a2, FieldPVCoordinates<T> pv2)
Linear constructor.
FieldPVCoordinates​(T a1, FieldPVCoordinates<T> pv1, T a2, FieldPVCoordinates<T> pv2, T a3, FieldPVCoordinates<T> pv3)
Linear constructor.
FieldPVCoordinates​(T a1, FieldPVCoordinates<T> pv1, T a2, FieldPVCoordinates<T> pv2, T a3, FieldPVCoordinates<T> pv3, T a4, FieldPVCoordinates<T> pv4)
Linear constructor.
FieldPVCoordinates​(T a, PVCoordinates pv)
Multiplicative constructor.
FieldPVCoordinates​(T a1, PVCoordinates pv1, T a2, PVCoordinates pv2)
Linear constructor.
FieldPVCoordinates​(T a1, PVCoordinates pv1, T a2, PVCoordinates pv2, T a3, PVCoordinates pv3)
Linear constructor.
FieldPVCoordinates​(T a1, PVCoordinates pv1, T a2, PVCoordinates pv2, T a3, PVCoordinates pv3, T a4, PVCoordinates pv4)
Linear constructor.
• ### Method Summary

All Methods
Modifier and Type Method Description
FieldPVCoordinates<T> blendArithmeticallyWith​(FieldPVCoordinates<T> other, T blendingValue)
FieldPVCoordinates<T> crossProduct​(FieldPVCoordinates<T> pv2)
Compute the cross-product of two instances.
static <T extends CalculusFieldElement<T>>FieldVector3D<T> estimateVelocity​(FieldVector3D<T> start, FieldVector3D<T> end, double dt)
Estimate velocity between two positions.
FieldVector3D<T> getAcceleration()
Gets the acceleration.
FieldVector3D<T> getAngularVelocity()
Get the angular velocity (spin) of this point as seen from the origin.
FieldVector3D<T> getMomentum()
Gets the momentum.
FieldVector3D<T> getPosition()
Gets the position.
FieldVector3D<T> getVelocity()
Gets the velocity.
static <T extends CalculusFieldElement<T>>FieldPVCoordinates<T> getZero​(Field<T> field)
Get fixed position/velocity at origin (both p, v and a are zero vectors).
FieldPVCoordinates<T> negate()
Get the opposite of the instance.
FieldPVCoordinates<T> normalize()
Normalize the position part of the instance.
FieldVector3D<T> positionShiftedBy​(T dt)
Get a time-shifted position.
FieldPVCoordinates<T> shiftedBy​(double dt)
Get a time-shifted state.
FieldPVCoordinates<T> shiftedBy​(T dt)
Get a time-shifted state.
FieldPVCoordinates<FieldDerivativeStructure<T>> toDerivativeStructurePV​(int order)
FieldVector3D<FieldDerivativeStructure<T>> toDerivativeStructureVector​(int order)
PVCoordinates toPVCoordinates()
Convert to a constant position-velocity.
String toString()
Return a string representation of this position/velocity pair.
FieldPVCoordinates<FieldUnivariateDerivative1<T>> toUnivariateDerivative1PV()
FieldVector3D<FieldUnivariateDerivative1<T>> toUnivariateDerivative1Vector()
FieldPVCoordinates<FieldUnivariateDerivative2<T>> toUnivariateDerivative2PV()
FieldVector3D<FieldUnivariateDerivative2<T>> toUnivariateDerivative2Vector()
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
• ### Constructor Detail

• #### FieldPVCoordinates

public FieldPVCoordinates​(FieldVector3D<T> position,
FieldVector3D<T> velocity)
Builds a FieldPVCoordinates triplet with zero acceleration.
Parameters:
position - the position vector (m)
velocity - the velocity vector (m/s)
• #### FieldPVCoordinates

public FieldPVCoordinates​(FieldVector3D<T> position,
FieldVector3D<T> velocity,
FieldVector3D<T> acceleration)
Builds a FieldPVCoordinates triplet.
Parameters:
position - the position vector (m)
velocity - the velocity vector (m/s)
acceleration - the acceleration vector (m/s²)
• #### FieldPVCoordinates

public FieldPVCoordinates​(Field<T> field,
PVCoordinates pv)
Builds a FieldPVCoordinates from a field and a regular PVCoordinates.
Parameters:
field - field for the components
pv - PVCoordinates triplet to convert
• #### FieldPVCoordinates

public FieldPVCoordinates​(double a,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(FieldPVCoordinates<T> start,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(double a1,
FieldPVCoordinates<T> pv1,
double a2,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
FieldPVCoordinates<T> pv1,
T a2,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
PVCoordinates pv1,
T 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(double a1,
FieldPVCoordinates<T> pv1,
double a2,
FieldPVCoordinates<T> pv2,
double a3,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
FieldPVCoordinates<T> pv1,
T a2,
FieldPVCoordinates<T> pv2,
T a3,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
PVCoordinates pv1,
T a2,
PVCoordinates pv2,
T 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(double a1,
FieldPVCoordinates<T> pv1,
double a2,
FieldPVCoordinates<T> pv2,
double a3,
FieldPVCoordinates<T> pv3,
double a4,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
FieldPVCoordinates<T> pv1,
T a2,
FieldPVCoordinates<T> pv2,
T a3,
FieldPVCoordinates<T> pv3,
T a4,
FieldPVCoordinates<T> 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(T a1,
PVCoordinates pv1,
T a2,
PVCoordinates pv2,
T a3,
PVCoordinates pv3,
T 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
• #### FieldPVCoordinates

public FieldPVCoordinates​(FieldVector3D<U> p)
Builds a FieldPVCoordinates triplet from a FieldVector3D<FieldDerivativeStructure>.

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
Since:
9.2
• ### Method Detail

• #### getZero

public static <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> getZero​(Field<T> field)
Get fixed position/velocity at origin (both p, v and a are zero vectors).
Type Parameters:
T - the type of the field elements
Parameters:
field - field for the components
Returns:
a new fixed position/velocity at origin
• #### toDerivativeStructureVector

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

The FieldDerivativeStructure 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
Since:
9.2
• #### toDerivativeStructurePV

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

The FieldDerivativeStructure 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<FieldUnivariateDerivative2<T>> toUnivariateDerivative2PV()
Transform the instance to a FieldPVCoordinates<FieldUnivariateDerivative2>.

The FieldUnivariateDerivative2 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 <T extends CalculusFieldElement<T>> FieldVector3D<T> estimateVelocity​(FieldVector3D<T> start,
FieldVector3D<T> 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.

Type Parameters:
T - the type of the field elements
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 FieldPVCoordinates<T> shiftedBy​(double dt)
Get a time-shifted state.

The state can be slightly shifted to close dates. This shift is based on a simple quadratic model. 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<T extends CalculusFieldElement<T>>
Parameters:
dt - time shift in seconds
Returns:
a new state, shifted with respect to the instance (which is immutable)
• #### shiftedBy

public FieldPVCoordinates<T> shiftedBy​(T dt)
Get a time-shifted state.

The state can be slightly shifted to close dates. This shift is based on a simple quadratic model. 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 FieldTimeShiftable<FieldPVCoordinates<T extends CalculusFieldElement<T>>,​T extends CalculusFieldElement<T>>
Parameters:
dt - time shift in seconds
Returns:
a new state, shifted with respect to the instance (which is immutable)
• #### positionShiftedBy

public FieldVector3D<T> positionShiftedBy​(T dt)
Get a time-shifted position. Same as shiftedBy(CalculusFieldElement) 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)
Since:
11.2
• #### getPosition

public FieldVector3D<T> getPosition()
Gets the position.
Returns:
the position vector (m).
• #### getVelocity

public FieldVector3D<T> getVelocity()
Gets the velocity.
Returns:
the velocity vector (m/s).
• #### getAcceleration

public FieldVector3D<T> getAcceleration()
Gets the acceleration.
Returns:
the acceleration vector (m/s²).
• #### getMomentum

public FieldVector3D<T> 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 FieldVector3D<T> 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 FieldPVCoordinates<T> negate()
Get the opposite of the instance.
Returns:
a new position-velocity which is opposite to the instance
• #### normalize

public FieldPVCoordinates<T> 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 FieldPVCoordinates<T> crossProduct​(FieldPVCoordinates<T> pv2)
Compute the cross-product of two instances.
Parameters:
pv2 - second instances
Returns:
the cross product v1 ^ v2 as a new instance
• #### toPVCoordinates

public PVCoordinates toPVCoordinates()
Convert to a constant position-velocity.
Returns:
a constant position-velocity
• #### 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
• #### blendArithmeticallyWith

public FieldPVCoordinates<T> blendArithmeticallyWith​(FieldPVCoordinates<T> other,
T blendingValue)
throws MathIllegalArgumentException
Specified by:
blendArithmeticallyWith in interface FieldBlendable<FieldPVCoordinates<T extends CalculusFieldElement<T>>,​T extends CalculusFieldElement<T>>
Throws:
MathIllegalArgumentException