Inertia

Functions
template<typename T , typename T2 >
void	EGXMath::EllipseInertia (const T massInkg, const T semiMajorAxisInm, const T semiMinorAxisInm, T2(&matrix)[9])
	Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis. \[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaHoop.html. More...
template<typename T , typename T2 >
void	EGXMath::EllipseInertia (const T massInkg, const T semiMajorAxisInm, const T semiMinorAxisInm, std::vector< T2 > &matrix)
	Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis. \[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaHoop.html. More...
template<typename T >
void	EGXMath::EllipseInertia (const T massInkg, const T semiMajorAxisInm, const T semiMinorAxisInm, glm::mat3 &matrix)
	Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis. \[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \] See https://en.wikipedia.org/wiki/List_of_moments_of_inertia and http://scienceworld.wolfram.com/physics/MomentofInertiaHoop.html. More...

Detailed Description

Function Documentation

EllipseInertia() [1/3]

template<typename T , typename T2 >

void EGXMath::EllipseInertia	(	const T	massInkg,
		const T	semiMajorAxisInm,
		const T	semiMinorAxisInm,
		T2(&)	matrix[9]
	)

Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis.

\[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \]

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

Parameters

massInkg	\( m\ (kg)\) Mass of the ellipse in kilograms.
semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm	\( b\ (m)\) Semi-minor axis of the ellipse in meters.
matrix	\( I_{ellipse}\ (kg\ m^2)\) Moment of inertia tensor matrix.

See also

EllipseSurfaceArea() for area of an ellipse.

EllipseCircumference() for circumference of an ellipse.

EllipseSemiMajorAxis() for semi-major axis of an ellipse.

EllipseSemiMinorAxis() for semi-minor axis of an ellipse.

EllipseSemiLatusRectum() for semi-latus rectum of an ellipse.

EllipseDirectrix() for directrix of an ellipse.

EllipseFocalParameter() for focal parameter of an ellipse.

EllipseFocalLength() for focal length of an ellipse.

EllipseLinearEccentricity() for linear eccentricity of an ellipse.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseInertia() [2/3]

template<typename T , typename T2 >

void EGXMath::EllipseInertia	(	const T	massInkg,
		const T	semiMajorAxisInm,
		const T	semiMinorAxisInm,
		std::vector< T2 > &	matrix
	)

Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis.

\[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \]

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

Parameters

massInkg	\( m\ (kg)\) Mass of the ellipse in kilograms.
semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm	\( b\ (m)\) Semi-minor axis of the ellipse in meters.
matrix	\( I_{ellipse}\ (kg\ m^2)\) Moment of inertia tensor matrix.

See also

EllipseSurfaceArea() for area of an ellipse.

EllipseCircumference() for circumference of an ellipse.

EllipseSemiMajorAxis() for semi-major axis of an ellipse.

EllipseSemiMinorAxis() for semi-minor axis of an ellipse.

EllipseSemiLatusRectum() for semi-latus rectum of an ellipse.

EllipseDirectrix() for directrix of an ellipse.

EllipseFocalParameter() for focal parameter of an ellipse.

EllipseFocalLength() for focal length of an ellipse.

EllipseLinearEccentricity() for linear eccentricity of an ellipse.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseInertia() [3/3]

template<typename T >

void EGXMath::EllipseInertia	(	const T	massInkg,
		const T	semiMajorAxisInm,
		const T	semiMinorAxisInm,
		glm::mat3 &	matrix
	)

Finds the moment of inertia tensor, \(I_{ellipse}\) of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\) that is infinitly thin. It is assumed that the semi-major axis lays on the x axis while semi-minor axis is on the y axis.

\[ I_{ellipse}=\begin{bmatrix} ??? & 0 & 0\\ 0 & ??? & 0\\ 0 & 0 & ??? \end{bmatrix} \]

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

Parameters

massInkg	\( m\ (kg)\) Mass of the ellipse in kilograms.
semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm	\( b\ (m)\) Semi-minor axis of the ellipse in meters.
matrix	\( I_{ellipse}\ (kg\ m^2)\) Moment of inertia tensor matrix.

See also

EllipseSurfaceArea() for area of an ellipse.

EllipseCircumference() for circumference of an ellipse.

EllipseSemiMajorAxis() for semi-major axis of an ellipse.

EllipseSemiMinorAxis() for semi-minor axis of an ellipse.

EllipseSemiLatusRectum() for semi-latus rectum of an ellipse.

EllipseDirectrix() for directrix of an ellipse.

EllipseFocalParameter() for focal parameter of an ellipse.

EllipseFocalLength() for focal length of an ellipse.

EllipseLinearEccentricity() for linear eccentricity of an ellipse.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.