Struct nalgebra_spacetime::MomentumN

pub struct MomentumN<N, D> where
    N: Scalar,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>,  { /* fields omitted */ }

Momentum in $n$-dimensional Lorentzian space $\R^{-,+} = \R^{1,n-1}$.

Assuming unit system with speed of light $c=1$ and rest mass $m$ as timelike norm in spacelike sign convention as in:

$$ m^2=E^2-\vec {p}^2=-p_\mu p^\mu $$

Where $p^\mu$ is the $n$-momentum with energy $E$ as temporal $p^0$ and momentum $\vec p$ as spatial $p^i$ components:

$$ p^\mu = m u^\mu = m \begin{pmatrix} \gamma \\ \gamma \vec \beta \end{pmatrix} = \begin{pmatrix} \gamma m = E \\ \gamma m \vec \beta = \vec p \end{pmatrix} $$

With $n$-velocity $u^\mu$, Lorentz factor $\gamma$, and velocity ratio $\vec \beta$.

Implementations

impl<N, D> MomentumN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

pub fn from_split(energy: &N, momentum: &VectorN<N, DimNameDiff<D, U1>>) -> Self where
    DefaultAllocator: Allocator<N, DimNameDiff<D, U1>>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: StorageMut<N, D, U1, RStride = U1, CStride = D>, 

Momentum with spacetime LorentzianN::split, energy $E$ and momentum $\vec p$.

pub fn from_mass_at_velocity(mass: N, velocity: VectorN<N, D>) -> Self where
    DefaultAllocator: Allocator<N, DimNameDiff<D, U1>>, 

Momentum $p^\mu=m u^\mu$ with rest mass $m$ at velocity $u^\mu$.

pub fn from_mass_in_frame(mass: N, frame: FrameN<N, D>) -> Self where
    DefaultAllocator: Allocator<N, DimNameDiff<D, U1>>, 

Momentum $p^\mu$ with rest mass $m$ in frame.

Equals frame.velocity() * mass.

pub fn from_mass_at_rest(mass: N) -> Self

Momentum $p^\mu$ with rest mass $m$ in center-of-momentum frame.

pub fn mass(&self) -> N

Rest mass $m$ as timelike norm $\sqrt{-p_\mu p^\mu}$ in spacelike sign convention.

pub fn velocity(&self) -> VectorN<N, D>

Velocity $u^\mu$ as momentum $p^\mu$ divided by rest mass() $m$.

pub fn energy(&self) -> &N

Energy $E$ as LorentzianN::temporal component.

pub fn momentum(&self) -> VectorSliceN<'_, N, DimNameDiff<D, U1>, U1, D> where
    DefaultAllocator: Allocator<N, D, U1>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Storage<N, D, U1, RStride = U1, CStride = D>, 

Momentum $\vec p$ as LorentzianN::spatial components.

Trait Implementations

impl<N, D> Add<MomentumN<N, D>> for MomentumN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Self

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<N: Clone, D: Clone> Clone for MomentumN<N, D> where
    N: Scalar,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

fn clone(&self) -> MomentumN<N, D>

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N, D> Copy for MomentumN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: Copy, 

impl<N: Debug, D: Debug> Debug for MomentumN<N, D> where
    N: Scalar,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<N, D> From<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for MomentumN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

fn from(momentum: VectorN<N, D>) -> Self

Performs the conversion.

impl<N, D> From<MomentumN<N, D>> for VectorN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

fn from(momentum: MomentumN<N, D>) -> Self

Performs the conversion.

impl<N: PartialEq, D: PartialEq> PartialEq<MomentumN<N, D>> for MomentumN<N, D> where
    N: Scalar,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

fn eq(&self, other: &MomentumN<N, D>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &MomentumN<N, D>) -> bool

This method tests for !=.

impl<N, D> StructuralPartialEq for MomentumN<N, D> where
    N: Scalar,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

impl<N, D> Sub<MomentumN<N, D>> for MomentumN<N, D> where
    N: SimdRealField + Signed + Real,
    D: DimNameSub<U1>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Self

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.