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```
```use std::ops::{Add, AddAssign, Mul, Neg};

use crate::algebra::{Force3, Velocity3};
use na::{self, Isometry3, Matrix3, Matrix6, RealField, U3};

/// The inertia of a rigid body grouping both its mass and its angular inertia.
#[derive(Clone, Copy, Debug)]
pub struct Inertia3<N: RealField> {
/// The linear part (mass) of the inertia.
pub linear: N,
/// The angular inertia.
pub angular: Matrix3<N>,
}

impl<N: RealField> Inertia3<N> {
/// Creates an inertia from its linear and angular components.
pub fn new(linear: N, angular: Matrix3<N>) -> Self {
Inertia3 { linear, angular }
}

/// Creates an inertia from its linear and angular components.
pub fn new_with_angular_matrix(linear: N, angular: Matrix3<N>) -> Self {
Self::new(linear, angular)
}

/// Get the mass.
pub fn mass(&self) -> N {
self.linear
}

/// Get the inverse mass.
///
/// Returns 0.0 if the mass is 0.0.
pub fn inv_mass(&self) -> N {
if self.linear.is_zero() {
N::zero()
} else {
self.linear
}
}

/// Create a zero inertia.
pub fn zero() -> Self {
Inertia3::new(na::zero(), na::zero())
}

/// Get the angular inertia tensor.
#[inline]
pub fn angular_matrix(&self) -> &Matrix3<N> {
&self.angular
}

/// Convert the inertia into a matrix where the mass is represented as a 3x3
/// diagonal matrix on the upper-left corner, and the angular part as a 3x3
/// matrix on the lower-rigth corner.
pub fn to_matrix(&self) -> Matrix6<N> {
let mut res = Matrix6::zeros();
res.fixed_slice_mut::<U3, U3>(3, 3).copy_from(&self.angular);

res.m11 = self.linear;
res.m22 = self.linear;
res.m33 = self.linear;

res
}

/// Compute the inertia on the given coordinate frame.
pub fn transformed(&self, i: &Isometry3<N>) -> Self {
let rot = i.rotation.to_rotation_matrix();
Inertia3::new(self.linear, rot * self.angular * rot.inverse())
}

/// Inverts this inetia matrix.
///
/// Sets the angular part to zero if it is not invertible.
pub fn inverse(&self) -> Self {
let inv_mass = if self.linear.is_zero() {
N::zero()
} else {
N::one() / self.linear
};
let inv_angular = self.angular.try_inverse().unwrap_or_else(na::zero);
Inertia3::new(inv_mass, inv_angular)
}
}

impl<N: RealField> Neg for Inertia3<N> {
type Output = Self;

#[inline]
fn neg(self) -> Self {
Self::new(-self.linear, -self.angular)
}
}

impl<N: RealField> Add<Inertia3<N>> for Inertia3<N> {
type Output = Inertia3<N>;

#[inline]
fn add(self, rhs: Inertia3<N>) -> Inertia3<N> {
Inertia3::new(self.linear + rhs.linear, self.angular + rhs.angular)
}
}

impl<N: RealField> AddAssign<Inertia3<N>> for Inertia3<N> {
#[inline]
fn add_assign(&mut self, rhs: Inertia3<N>) {
self.linear += rhs.linear;
self.angular += rhs.angular;
}
}

impl<N: RealField> Mul<Velocity3<N>> for Inertia3<N> {
type Output = Force3<N>;

#[inline]
fn mul(self, rhs: Velocity3<N>) -> Force3<N> {
Force3::new(rhs.linear * self.linear, self.angular * rhs.angular)
}
}

// NOTE: This is meaningful when `self` is the inverse inertia.
impl<N: RealField> Mul<Force3<N>> for Inertia3<N> {
type Output = Velocity3<N>;

#[inline]
fn mul(self, rhs: Force3<N>) -> Velocity3<N> {
Velocity3::new(rhs.linear * self.linear, self.angular * rhs.angular)
}
}
```