Inertia

Functions
template<typename T , typename T2 >
void	EGXMath::EllipsoidInertia (const T mass, const T aSemiPrincipleAxisInm, const T bSemiPrincipleAxisInm, const T cSemiPrincipleAxisInm, T2(&matrix)[9])
	Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis. \[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html. More...
template<typename T , typename T2 >
void	EGXMath::EllipsoidInertia (const T mass, const T aSemiPrincipleAxisInm, const T bSemiPrincipleAxisInm, const T cSemiPrincipleAxisInm, std::vector< T2 > &matrix)
	Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis. \[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html. More...
template<typename T >
void	EGXMath::EllipsoidInertia (const T mass, const T aSemiPrincipleAxisInm, const T bSemiPrincipleAxisInm, const T cSemiPrincipleAxisInm, glm::mat3 &matrix)
	Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis. \[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html. More...

Detailed Description

Function Documentation

EllipsoidInertia() [1/3]

template<typename T , typename T2 >

void EGXMath::EllipsoidInertia	(	const T	mass,
		const T	aSemiPrincipleAxisInm,
		const T	bSemiPrincipleAxisInm,
		const T	cSemiPrincipleAxisInm,
		T2(&)	matrix[9]
	)

Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis.

\[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \]

See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html.

Parameters

mass	\( m\ (kg)\) Mass of the ellipsoid.
aSemiPrincipleAxisInm	\( a\ (m)\) Semi-principle axis of the ellipsoid that lays along the x-axis in meters.
bSemiPrincipleAxisInm	\( b\ (m)\) Semi-principle axis of the ellipsoid that lays along the y-axis in meters.
cSemiPrincipleAxisInm	\( c\ (m)\) Semi-principle axis of the ellipsoid that lays along the z-axis in meters.
matrix	\( I_{ellipsoid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the ellipsoid.

See also

EllipsoidSurfaceArea() for surface area of an ellipsoid.

EllipsoidVolume() for volume of an ellipsoid.

SphereInertia() for inertial tensor of a sphere.

SpheroidInertia() for inertial tensor of a spheroid.

EllipsoidInertia() [2/3]

template<typename T , typename T2 >

void EGXMath::EllipsoidInertia	(	const T	mass,
		const T	aSemiPrincipleAxisInm,
		const T	bSemiPrincipleAxisInm,
		const T	cSemiPrincipleAxisInm,
		std::vector< T2 > &	matrix
	)

Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis.

\[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \]

See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html.

Parameters

mass	\( m\ (kg)\) Mass of the ellipsoid.
aSemiPrincipleAxisInm	\( a\ (m)\) Semi-principle axis of the ellipsoid that lays along the x-axis in meters.
bSemiPrincipleAxisInm	\( b\ (m)\) Semi-principle axis of the ellipsoid that lays along the y-axis in meters.
cSemiPrincipleAxisInm	\( c\ (m)\) Semi-principle axis of the ellipsoid that lays along the z-axis in meters.
matrix	\( I_{ellipsoid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the ellipsoid.

See also

EllipsoidSurfaceArea() for surface area of an ellipsoid.

EllipsoidVolume() for volume of an ellipsoid.

SphereInertia() for inertial tensor of a sphere.

SpheroidInertia() for inertial tensor of a spheroid.

EllipsoidInertia() [3/3]

template<typename T >

void EGXMath::EllipsoidInertia	(	const T	mass,
		const T	aSemiPrincipleAxisInm,
		const T	bSemiPrincipleAxisInm,
		const T	cSemiPrincipleAxisInm,
		glm::mat3 &	matrix
	)

Finds the moment of inertia tensor, \(I_{ellipsoid}\) of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). It is assumed that \(a\) lays on the x-axis, \(b\) on the y-axis and \(c\) on the z-axis.

\[ I_{ellipsoid}=\begin{bmatrix} \frac{1}{5}m\ b^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{1}{5}m\ a^2b^2 \end{bmatrix} \]

See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html.

Parameters

mass	\( m\ (kg)\) Mass of the ellipsoid.
aSemiPrincipleAxisInm	\( a\ (m)\) Semi-principle axis of the ellipsoid that lays along the x-axis in meters.
bSemiPrincipleAxisInm	\( b\ (m)\) Semi-principle axis of the ellipsoid that lays along the y-axis in meters.
cSemiPrincipleAxisInm	\( c\ (m)\) Semi-principle axis of the ellipsoid that lays along the z-axis in meters.
matrix	\( I_{ellipsoid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the ellipsoid.

See also

EllipsoidSurfaceArea() for surface area of an ellipsoid.

EllipsoidVolume() for volume of an ellipsoid.

SphereInertia() for inertial tensor of a sphere.

SpheroidInertia() for inertial tensor of a spheroid.