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Inertia

inertia.hpp provides two types:

  • LibXR::Inertia<Scalar>: rigid-body inertia tensor plus mass
  • LibXR::CenterOfMass<Scalar>: center-of-mass position plus mass

Like the types described on the Transform page, this group is also gated by LIBXR_NO_EIGEN.

1. Inertia<Scalar>​

1.1 Data layout​

Inertia<Scalar> exposes two public pieces of data:

  • data[9]: the 3x3 inertia tensor
  • mass: the mass value

Default construction initializes:

  • mass = 0
  • data to zero

1.2 Construction forms​

The main construction forms are:

  • Inertia(mass, data[9])
  • Inertia(mass, matrix[3][3])
  • Inertia(mass, arr[6])
  • Inertia(mass, xx, yy, zz, xy, yz, xz)
  • Inertia(mass, Eigen::Matrix<Scalar, 3, 3>)

The 6-value and 7-argument forms take the principal moments and products of inertia in the order xx, yy, zz, xy, yz, xz and store the negated products as off-diagonal elements (for example, element (0, 1) is -xy); the 9-element array, 3x3 array, and Eigen matrix forms store the full tensor as given.

1.3 Main operations​

  • conversion to Eigen::Matrix<Scalar, 3, 3>
  • operator()(i, j) for element access
  • operator+ with another 3x3 matrix
  • Translate(p) for inertia translation
  • Rotate(R) for rotation by a matrix
  • Rotate(q) for rotation by a quaternion

These operations are mainly used to move local inertia information into another pose or reference point.

2. CenterOfMass<Scalar>​

CenterOfMass<Scalar> represents a center of mass as “position + mass”.

Its public data members are:

  • position
  • mass

Common construction forms:

  • CenterOfMass(mass, Position)
  • CenterOfMass(mass, Eigen::Matrix<3,1>)
  • CenterOfMass(inertia, transform)

It also provides:

  • operator+
  • operator+=

which can be used to accumulate multiple rigid-body centers of mass into a total result.

3. Example​

#include <libxr.hpp>

LibXR::Inertia<> body_inertia(1.5, 0.02, 0.03, 0.04, 0.0, 0.0, 0.0);

LibXR::Position<> offset(0.1, 0.0, 0.0);
auto moved = body_inertia.Translate(offset);

LibXR::Quaternion<> q = LibXR::EulerAngle<>(0.0, 0.0, 1.57).ToQuaternion();
auto rotated = moved.Rotate(q);

LibXR::Transform<> pose(q, LibXR::Position<>(0.2, 0.0, 0.0));
LibXR::CenterOfMass<> cog(rotated, pose);

4. Usage guidance​

  • For geometry and pose only, Transform / Quaternion / RotationMatrix are enough; Inertia is needed when mass distribution, center of mass, or inertia conversion matters.
  • Translate() and Rotate() return new inertia objects, which fits transformation-chain style calculations well.
  • When the build disables Eigen through LIBXR_NO_EIGEN, these types are unavailable and should not be part of public module boundaries.