MBSVT: D:/Mis_Documentos/investigacion/proyectos/VT optimization project/MBSVT/trunk/math

Modules
module	math_oper
	Module of non-intrinsic mathematical operations. Contains all the operations necessary for multi body dynamics computations not supported by the Fortran 2003 standard.
Functions/Subroutines
REAL(8)	math_oper::norm (r)
	Calculate the standard $\left\|{\bf r}\right\|$ of a vector $\bf r$ .
REAL(8), dimension(size(r))	math_oper::normalize (r)
	Normalize an vector ${\bf normalize(r)}=\frac{\bf r}{\left\|{\bf r}\right\|}$ .
REAL(8), dimension(3)	math_oper::pvect (u, v)
	Calculates the cross product of two vectors.
subroutine	math_oper::PerpVectors (nfl, u, v)
	Given a vector, calculates two perpendicular vectors to the given one.
real(8)	math_oper::MREulerParam (e)
	Given the vector of Euler parameters ${\bf p}$ , it returns the rotation transformation matrix ${\bf A}$ .
real(8)	math_oper::Atp_v (p, v)
	Given the vector of Euler parameters ${\bf p}$ , it returns the matrix ${\bf A}$ .
real(8)	math_oper::Gmatrix (e)
	Given the vector of Euler parameters , it returns the G matrix .
real(8)	math_oper::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)	math_oper::dMREulerParam_v (e, v)
	Given the vector of Euler parameters and a vecter , it returns $\frac{\partial Av}{\partial e}$ .
real(8)	math_oper::dMREulerParam_t (p, pd, t)
	Given the vector of Euler parameters , the velocity vector of Euler parameters $\dot e$ and a vector , it returns $\frac{\mathrm{d} Av}{\mathrm{d} t}$ .
real(8)	math_oper::d2MREulerParam_t2 (p, pd, ps, t)
	Given the vector of Euler parameters , the velocity vector of Euler parameters $\dot e$ and a vector , it returns $\frac{\mathrm{d}^2 Av}{\mathrm{d} t^2}$ .
real(8)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::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)	math_oper::dMREulerParam_v_e1 (e, v)
	Given the vector of Euler parameters and a vecter , it returns $\partial (\frac{\partial Av}{\partial e})\partial e_0$ .
real(8)	math_oper::dMREulerParam_v_e2 (e, v)
	Given the vector of Euler parameters and a vecter , it returns $\partial (\frac{\partial Av}{\partial e})\partial e_1$ .
real(8)	math_oper::dMREulerParam_v_e3 (e, v)
	Given the vector of Euler parameters and a vecter , it returns $\partial (\frac{\partial Av}{\partial e})\partial e_2$ .
real(8)	math_oper::dMREulerParam_v_e4 (e, v)
	Given the vector of Euler parameters and a vecter , it returns $\partial (\frac{\partial Av}{\partial e})\partial e_3$ .
real(8)	math_oper::MREulerParam_e1 (e)
	Given the vector of Euler parameters , it returns the derivative of the rotation matrix with respect to .
real(8)	math_oper::MREulerParam_e2 (e)
	Given the vector of Euler parameters , it returns the derivative of the rotation matrix with respect to .
real(8)	math_oper::MREulerParam_e3 (e)
	Given the vector of Euler parameters , it returns the derivative of the rotation matrix with respect to .
real(8)	math_oper::MREulerParam_e4 (e)
	Given the vector of Euler parameters , it returns the derivative of the rotation matrix with respect to .
real(8), dimension(size(u), size(v))	math_oper::tensor_product (u, v)
	Given the two vectors, find the tensor product between these two vectors.
real(8), dimension(3, 3)	math_oper::skew (a)
	Given one vector, find the skew symmetric matrix for this vector.
Variables
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(3, 3), parameter	math_oper::ZEROS3 = 0.d0
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])

Modules

Functions/Subroutines

Variables