MBSVT 1.0
Functions/Subroutines | Variables
math_oper Module Reference

Module of non-intrinsic mathematical operations. Contains all the operations necessary for multi body dynamics computations not supported by the Fortran 2003 standard. More...

Functions/Subroutines

REAL(8) norm (r)
 Calculate the standard $ \left|{\bf r}\right| $ of a vector $ \bf r $.
REAL(8), dimension(size(r)) normalize (r)
 Normalize an vector ${\bf normalize(r)}=\frac{\bf r}{\left|{\bf r}\right|}$.
REAL(8), dimension(3) pvect (u, v)
 Calculates the cross product of two vectors.
subroutine PerpVectors (nfl, u, v)
 Given a vector, calculates two perpendicular vectors to the given one.
real(8) MREulerParam (e)
 Given the vector of Euler parameters $ {\bf p}$, it returns the rotation transformation matrix $ {\bf A}$.
real(8) Atp_v (p, v)
 Given the vector of Euler parameters $ {\bf p}$, it returns the matrix $ {\bf A}$.
real(8) Gmatrix (e)
 Given the vector of Euler parameters $e$, it returns the G matrix $G$.
real(8) Gtp_v (v)
 Given the vector of Euler parameters $ {\bf p}$ and a vector $ {\bf v}$, it returns the ${\bf G}^{\rm T}{\bf v}$ matrix.
real(8) dMREulerParam_v (e, v)
 Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\frac{\partial Av}{\partial e}$.
real(8) dMREulerParam_t (p, pd, t)
 Given the vector of Euler parameters $e$, the velocity vector of Euler parameters $\dot e$ and a vector $v$, it returns $\frac{\mathrm{d} Av}{\mathrm{d} t}$.
real(8) d2MREulerParam_t2 (p, pd, ps, t)
 Given the vector of Euler parameters $e$, the velocity vector of Euler parameters $\dot e$ and a vector $v$, it returns $\frac{\mathrm{d}^2 Av}{\mathrm{d} t^2}$.
real(8) dMREulerParam_t_e1 (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_0}$.
real(8) dMREulerParam_t_e2 (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_1}$.
real(8) dMREulerParam_t_e3 (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_2}$.
real(8) dMREulerParam_t_e4 (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_3}$.
real(8) dMREulerParam_t_e1d (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_0}$.
real(8) dMREulerParam_t_e2d (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_1}$.
real(8) dMREulerParam_t_e3d (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_2}$.
real(8) dMREulerParam_t_e4d (p, pd, t)
 Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_3}$.
real(8) dMREulerParam_v_e1 (e, v)
 Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_0$.
real(8) dMREulerParam_v_e2 (e, v)
 Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_1$.
real(8) dMREulerParam_v_e3 (e, v)
 Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_2$.
real(8) dMREulerParam_v_e4 (e, v)
 Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_3$.
real(8) MREulerParam_e1 (e)
 Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_0$.
real(8) MREulerParam_e2 (e)
 Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_1$.
real(8) MREulerParam_e3 (e)
 Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_2$.
real(8) MREulerParam_e4 (e)
 Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_3$.
real(8), dimension(size(u),
size(v)) 		tensor_product (u, v)
 Given the two vectors, find the tensor product between these two vectors.
real(8), dimension(3, 3) skew (a)
 Given one vector, find the skew symmetric matrix for this vector.

Variables

REAL(8), dimension(3, 3), parameter EYE3 = RESHAPE(SOURCE=(/ 1.d0,0.d0,0.d0, 0.d0,1.d0,0.d0, 0.d0,0.d0,1.d0/), SHAPE=(/3,3/))
REAL(8), dimension(3, 3), parameter ZEROS3 = 0.d0
REAL(8), dimension(4, 4), parameter EYE4 = RESHAPE(SOURCE=(/ 1.d0,0.d0,0.d0,0.d0, 0.d0,1.d0,0.d0,0.d0, 0.d0,0.d0,1.d0,0.d0, 0.d0,0.d0,0.d0,1.d0/), SHAPE=(/4,4/))
REAL(8), dimension(3, 4), parameter Gmatrix_p1 = reshape([0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0], [3, 4])
REAL(8), dimension(3, 4), parameter Gmatrix_p2 = reshape([-1.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, -1.d0, 0.d0, 1.d0, 0.d0], [3, 4])
REAL(8), dimension(3, 4), parameter Gmatrix_p3 = reshape([0.d0, -1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, -1.d0, 0.d0, 0.d0], [3, 4])
REAL(8), dimension(3, 4), parameter Gmatrix_p4 = reshape([0.d0, 0.d0, -1.d0, 0.d0, -1.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0], [3, 4])

Detailed Description

Module of non-intrinsic mathematical operations. Contains all the operations necessary for multi body dynamics computations not supported by the Fortran 2003 standard.

Function/Subroutine Documentation

real(8) math_oper::Atp_v ( real(8),dimension(4),intent(in)  p,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $ {\bf p}$, it returns the matrix $ {\bf A}$.

Parameters:
evector of Euler parameters.
real(8) math_oper::d2MREulerParam_t2 ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(4),intent(in)  ps,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters $e$, the velocity vector of Euler parameters $\dot e$ and a vector $v$, it returns $\frac{\mathrm{d}^2 Av}{\mathrm{d} t^2}$.

Parameters:
pvector of Euler parameters.
pdvector of the first derivative of Euler parameters.
psvector of the second derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters $e$, the velocity vector of Euler parameters $\dot e$ and a vector $v$, it returns $\frac{\mathrm{d} Av}{\mathrm{d} t}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e1 ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_0}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e1d ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_0}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e2 ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_1}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e2d ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_1}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e3 ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_2}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e3d ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_2}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e4 ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{e_3}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_t_e4d ( real(8),dimension(4),intent(in)  p,
real(8),dimension(4),intent(in)  pd,
real(8),dimension(3),intent(in)  t 
)

Given the vector of Euler parameters, the velocity vector of Euler parameters and a vector, it returns $\partial{\frac{\mathrm{d} Av}{\mathrm{d} t}}\partial{\dot e_3}$.

Parameters:
pvector of Euler parameters.
pdvector of the derivative of Euler parameters.
tvector given in the body reference frame.
real(8) math_oper::dMREulerParam_v ( real(8),dimension(4),intent(in)  e,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\frac{\partial Av}{\partial e}$.

Parameters:
evector of Euler parameters.
vvector given in the body reference frame.
real(8) math_oper::dMREulerParam_v_e1 ( real(8),dimension(4),intent(in)  e,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_0$.

Parameters:
evector of Euler parameters.
vvector given in the body reference frame.
real(8) math_oper::dMREulerParam_v_e2 ( real(8),dimension(4),intent(in)  e,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_1$.

Parameters:
evector of Euler parameters.
vvector given in the body reference frame.
real(8) math_oper::dMREulerParam_v_e3 ( real(8),dimension(4),intent(in)  e,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_2$.

Parameters:
evector of Euler parameters.
vvector given in the body reference frame.
real(8) math_oper::dMREulerParam_v_e4 ( real(8),dimension(4),intent(in)  e,
real(8),dimension(3),intent(in)  v 
)

Given the vector of Euler parameters $e$ and a vecter $v$, it returns $\partial (\frac{\partial Av}{\partial e})\partial e_3$.

Parameters:
evector of Euler parameters.
vvector given in the body reference frame.
real(8) math_oper::Gmatrix ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $e$, it returns the G matrix $G$.

Parameters:
evector of Euler parameters.
real(8) math_oper::Gtp_v ( real(8),dimension(3),intent(in)  v)

Given the vector of Euler parameters $ {\bf p}$ and a vector $ {\bf v}$, it returns the ${\bf G}^{\rm T}{\bf v}$ matrix.

Parameters:
pvector of Euler parameters.
real(8) math_oper::MREulerParam ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $ {\bf p}$, it returns the rotation transformation matrix $ {\bf A}$.

Parameters:
pvector of Euler parameters.
real(8) math_oper::MREulerParam_e1 ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_0$.

Parameters:
evector of Euler parameters.
real(8) math_oper::MREulerParam_e2 ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_1$.

Parameters:
evector of Euler parameters.
real(8) math_oper::MREulerParam_e3 ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_2$.

Parameters:
evector of Euler parameters.
real(8) math_oper::MREulerParam_e4 ( real(8),dimension(4),intent(in)  e)

Given the vector of Euler parameters $e$, it returns the derivative of the rotation matrix with respect to $e_3$.

Parameters:
evector of Euler parameters.
REAL(8) math_oper::norm ( REAL(8),dimension(:)  r)

Calculate the standard $ \left|{\bf r}\right| $ of a vector $ \bf r $.

Parameters:
rvector.
REAL(8),dimension(size(r)) math_oper::normalize ( REAL(8),dimension(:)  r)

Normalize an vector ${\bf normalize(r)}=\frac{\bf r}{\left|{\bf r}\right|}$.

Parameters:
rvector
subroutine math_oper::PerpVectors ( REAL(8),dimension(3),intent(in)  nfl,
REAL(8),dimension(3),intent(out)  u,
REAL(8),dimension(3),intent(out)  v 
)

Given a vector, calculates two perpendicular vectors to the given one.

Parameters:
nflgiven vector.

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REAL(8),dimension(3) math_oper::pvect ( REAL(8),dimension(:),intent(in)  u,
REAL(8),dimension(:),intent(in)  v 
)

Calculates the cross product of two vectors.

Parameters:
u,vvectors involved.
real(8),dimension(3,3) math_oper::skew ( real(8),dimension(3),intent(in)  a)

Given one vector, find the skew symmetric matrix for this vector.

Parameters:
athe input vector
real(8),dimension(size(u),size(v)) math_oper::tensor_product ( real(8),dimension(:)  u,
real(8),dimension(:)  v 
)

Given the two vectors, find the tensor product between these two vectors.

Parameters:
uthe first vector
vthe second vector

Variable Documentation

REAL(8),dimension(3,3),parameter math_oper::EYE3 = RESHAPE(SOURCE=(/ 1.d0,0.d0,0.d0, 0.d0,1.d0,0.d0, 0.d0,0.d0,1.d0/), SHAPE=(/3,3/))
REAL(8),dimension(4,4),parameter math_oper::EYE4 = RESHAPE(SOURCE=(/ 1.d0,0.d0,0.d0,0.d0, 0.d0,1.d0,0.d0,0.d0, 0.d0,0.d0,1.d0,0.d0, 0.d0,0.d0,0.d0,1.d0/), SHAPE=(/4,4/))
REAL(8),dimension(3,4),parameter math_oper::Gmatrix_p1 = reshape([0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0], [3, 4])
REAL(8),dimension(3,4),parameter math_oper::Gmatrix_p2 = reshape([-1.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0, -1.d0, 0.d0, 1.d0, 0.d0], [3, 4])
REAL(8),dimension(3,4),parameter math_oper::Gmatrix_p3 = reshape([0.d0, -1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, -1.d0, 0.d0, 0.d0], [3, 4])
REAL(8),dimension(3,4),parameter math_oper::Gmatrix_p4 = reshape([0.d0, 0.d0, -1.d0, 0.d0, -1.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 0.d0, 0.d0], [3, 4])
REAL(8),dimension(3,3),parameter math_oper::ZEROS3 = 0.d0
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