Scott wrote: > .T turns the column vector into a row vector. > > The integrands that involve the rotation tensors are functions of t or > x , not both. > > int^x1_x0 int ^t0_t1 (dot(del_a(t)).T* R *b ) dt dx = > (x1-x0)( del_a(t1).T-del_a(t0).T )* R* b = > scalar > > I will test drive the galgebra module tonight. Is your sample code > complete? It did not run (with sagge-python and ipyhton from sage) > when I pasted it into a new file. > > > V/R > > Scott > > On Dec 3, 11:17 am, Alan Bromborsky<abro...@verizon.net> wrote: > >> Alan Bromborsky wrote: >> >>> Scott wrote: >>> >> >>>> My integral has several pieces like this: >>>> >> >>>> int^x1_x0 int ^t0_t1 (dot(del_a(t)).T* R *b ) dt dx >>>> >> >>>> del_a is 3*1, b is 3*1 and R is 3*3 rotation tensor( or a non >>>> orthogonal velocity transformation tensor H) >>>> >> >>>> R,H and b are are constant over the interval of integration. >>>> R=H inv(H.T) >>>> >> >>>> My goal is to perform symbolic manipulations, plug in basis functions >>>> and do collections in del_a R b form while preserving the vector >>>> orientations. >>>> >> >>>> With del_a linear (C1) in time the answer should be: (x1-x0)(del_a >>>> (t1).T-del_a(t0).T)* R* b = scalar >>>> At this time all the pieces are added together and collected wrt the >>>> del terms yielding a nonlinear system. At this point the tensors are >>>> populated. >>>> >> >>>> On Dec 1, 3:28 pm, Scott<scotta_2...@yahoo.com> wrote: >>>> >> >>>>> Is there a sympy function for making symbolic tensors? >>>>> Basically I want to treat 3x3 rotation tensor symbol that is constant >>>>> inside of an integral while preserving the tensor algebra (A*B .ne. >>>>> B*A). The 3x3 rotain tensor is multiplied by a 3x1 position tenosr >>>>> which is integrated. >>>>> >> >>>>> Is there a built in function for converting a 3*1 tensor to a skew >>>>> antisymetric cross product matrix then back again? >>>>> V/R >>>>> >> >>>>> Scott >>>>> >> >>>> -- >>>> >> >>>> You received this message because you are subscribed to the Google Groups >>>> "sympy" group. >>>> To post to this group, send email to sy...@googlegroups.com. >>>> To unsubscribe from this group, send email to >>>> sympy+unsubscr...@googlegroups.com. >>>> For more options, visit this group >>>> athttp://groups.google.com/group/sympy?hl=en. >>>> >> >>> Where is the position (x) dependence in the intergrand? >>> >> >>> -- >>> >> >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To post to this group, send email to sy...@googlegroups.com. >>> To unsubscribe from this group, send email to >>> sympy+unsubscr...@googlegroups.com. >>> For more options, visit this group >>> athttp://groups.google.com/group/sympy?hl=en. >>> >> Also what is T? >> > -- > > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sy...@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > > > The example is complete (If you have the copy that contains cos(a) or sin(a) it is wrong. All angles should be the half angle, a/2). I used the latest git of sympy and used ubuntu 9.10. Note that numpy must be installed for the GA module to work.
In my example then would a = a(x,t) (a is the rotation angle) and u = u(x,t) (u the axis of rotation) contain the x or t dependence? -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sy...@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
