Inertia

Functions
template<typename T , typename T2 >
void	EGXMath::SpheroidInertia (const T mass, const T equatorialRadiusInm, const T polarRadiusInm, T2(&matrix)[9])
	Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis. \[ I_{spheroid}=\begin{bmatrix} \frac{1}{5}m\ a^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{2}{5}m\ a^2 \end{bmatrix} \] 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::SpheroidInertia (const T mass, const T equatorialRadiusInm, const T polarRadiusInm, std::vector< T2 > &matrix)
	Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis. \[ I_{spheroid}=\begin{bmatrix} \frac{1}{5}m\ a^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{2}{5}m\ a^2 \end{bmatrix} \] 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::SpheroidInertia (const T mass, const T equatorialRadiusInm, const T polarRadiusInm, glm::mat3 &matrix)
	Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis. \[ I_{spheroid}=\begin{bmatrix} \frac{1}{5}m\ a^2c^2 & 0 & 0\\ 0 & \frac{1}{5}m\ a^2c^2 & 0\\ 0 & 0 & \frac{2}{5}m\ a^2 \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html. More...

Detailed Description

Function Documentation

SpheroidInertia() [1/3]

template<typename T , typename T2 >

void EGXMath::SpheroidInertia	(	const T	mass,
		const T	equatorialRadiusInm,
		const T	polarRadiusInm,
		T2(&)	matrix[9]
	)

Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis.

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

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.
equatorialRadiusInm	\( a\ (m)\) Equatorial radius in meters. The degenerate semi-principle axis of the spheroid.
polarRadiusInm	\( c\ (m)\) Polar radius in meters. The unique semi-principle axis of the spheroid.
matrix	\( I_{spheroid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the spheroid.

See also

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius of a spheroid.

SpheroidFlattening() for flattening of a spheroid.

SpheroidPolarRadius() for polar radius of a spheroid.

SpheroidSurfaceArea() for surface area of a spheroid.

SpheroidVolume() for volume of a spheroid.

SphereInertia() for inertial tensor of a sphere.

EllipsoidInertia() for inertial tensor of an ellipsoid.

SpheroidInertia() [2/3]

template<typename T , typename T2 >

void EGXMath::SpheroidInertia	(	const T	mass,
		const T	equatorialRadiusInm,
		const T	polarRadiusInm,
		std::vector< T2 > &	matrix
	)

Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis.

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

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.
equatorialRadiusInm	\( a\ (m)\) Equatorial radius in meters. The degenerate semi-principle axis of the spheroid.
polarRadiusInm	\( c\ (m)\) Polar radius in meters. The unique semi-principle axis of the spheroid.
matrix	\( I_{spheroid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the spheroid.

See also

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius of a spheroid.

SpheroidFlattening() for flattening of a spheroid.

SpheroidPolarRadius() for polar radius of a spheroid.

SpheroidSurfaceArea() for surface area of a spheroid.

SpheroidVolume() for volume of a spheroid.

SphereInertia() for inertial tensor of a sphere.

EllipsoidInertia() for inertial tensor of an ellipsoid.

SpheroidInertia() [3/3]

template<typename T >

void EGXMath::SpheroidInertia	(	const T	mass,
		const T	equatorialRadiusInm,
		const T	polarRadiusInm,
		glm::mat3 &	matrix
	)

Finds the moment of inertia tensor, \(I_{spheroid}\) of a spheroid with equatorial radius \(a\) and polar radius, \(c\). It is assumed that \(a\) lays on the xy-plane, and \(c\) on the z-axis.

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

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.
equatorialRadiusInm	\( a\ (m)\) Equatorial radius in meters. The degenerate semi-principle axis of the spheroid.
polarRadiusInm	\( c\ (m)\) Polar radius in meters. The unique semi-principle axis of the spheroid.
matrix	\( I_{spheroid}\ (kg\ m^2)\) Moment of inertia tensor matrix of the spheroid.

See also

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius of a spheroid.

SpheroidFlattening() for flattening of a spheroid.

SpheroidPolarRadius() for polar radius of a spheroid.

SpheroidSurfaceArea() for surface area of a spheroid.

SpheroidVolume() for volume of a spheroid.

SphereInertia() for inertial tensor of a sphere.

EllipsoidInertia() for inertial tensor of an ellipsoid.