EGXPhys
Functions
Disk
EGXMath Library » Geometry » 3D Objects

Functions

template<typename T , typename T2 >
void EGXMath::DiskInertia (const T mass, const T height, const T radius, T2(&matrix)[9])
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 
template<typename T , typename T2 >
void EGXMath::DiskThinInertia (const T mass, const T radius, T2(&matrix)[9])
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 
template<typename T , typename T2 >
void EGXMath::DiskInertia (const T mass, const T height, const T radius, std::vector< T2 > &matrix)
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 
template<typename T , typename T2 >
void EGXMath::DiskThinInertia (const T mass, const T radius, std::vector< T2 > &matrix)
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 
template<typename T , typename T2 >
void EGXMath::DiskInertia (const T mass, const T height, const T radius, glm::mat3 &matrix)
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 
template<typename T >
void EGXMath::DiskThinInertia (const T mass, const T radius, glm::mat3 &matrix)
 Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

 

Detailed Description

Function Documentation

◆ DiskInertia() [1/3]

template<typename T , typename T2 >
void EGXMath::DiskInertia ( const T  mass,
const T  height,
const T  radius,
T2(&)  matrix[9] 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
height\( r\ (m)\) Height of disk in meters.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CylinderInertia() for alias.
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
SphereInertia() for inertial tensor of a sphere.

◆ DiskInertia() [2/3]

template<typename T , typename T2 >
void EGXMath::DiskInertia ( const T  mass,
const T  height,
const T  radius,
std::vector< T2 > &  matrix 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
height\( r\ (m)\) Height of disk in meters.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CylinderInertia() for alias.
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
SphereInertia() for inertial tensor of a sphere.

◆ DiskInertia() [3/3]

template<typename T , typename T2 >
void EGXMath::DiskInertia ( const T  mass,
const T  height,
const T  radius,
glm::mat3 &  matrix 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), height, \(h\) and mass \(m\). Also known as a cylinder. The circular componet lays in the x,y plane.

\[ I_{disk}=\begin{bmatrix} \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{12}m\ h^2 + \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
height\( r\ (m)\) Height of disk in meters.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CylinderInertia() for alias.
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
SphereInertia() for inertial tensor of a sphere.

◆ DiskThinInertia() [1/3]

template<typename T , typename T2 >
void EGXMath::DiskThinInertia ( const T  mass,
const T  radius,
T2(&)  matrix[9] 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
CylinderInertia() for inertial tensor of a cylinder.
SphereInertia() for inertial tensor of a sphere.

◆ DiskThinInertia() [2/3]

template<typename T , typename T2 >
void EGXMath::DiskThinInertia ( const T  mass,
const T  radius,
std::vector< T2 > &  matrix 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
CylinderInertia() for inertial tensor of a cylinder.
SphereInertia() for inertial tensor of a sphere.

◆ DiskThinInertia() [3/3]

template<typename T >
void EGXMath::DiskThinInertia ( const T  mass,
const T  radius,
glm::mat3 &  matrix 
)

Finds the moment of inertia tensor, \(I_{disk}\) of a disk with radius, \(r\), and mass \(m\) that is infinitly thin.

\[ I_{disk}=\begin{bmatrix} \frac{1}{4}m\ r^2 & 0 & 0\\ 0 & \frac{1}{4}m\ r^2 & 0\\ 0 & 0 & \frac{1}{2}m\ r^2 \end{bmatrix} \]

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

Parameters
mass\( m\ (kg)\) Mass of disk in kilograms.
radius\( r\ (m)\) Radius of disk in meters.
matrix\( I_{disk}\ (kg\ m^2)\) Inertia tensor matrix in kilograms meter squared.
See also
CircleSurfaceArea() for area of a circle.
CircleCircumference() for circumference of a circle.
HoopThinInertia() for inertial tensor of a thin hoop.
HoopInertia() for inertial tensor of a hoop.
DiskThinInertia() for inertial tensor of a thin disk.
DiskInertia() for inertial tensor of a disk.
CylinderInertia() for inertial tensor of a cylinder.
SphereInertia() for inertial tensor of a sphere.