Pawan Takhar

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15 years, 211 days

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These are replies submitted by Pawan Takhar

Joe, When I put % in front of the user defined function, it started behaving like an inert function. E.g. if function f is defined, %f behaves as inert and value command can evaluate the function. Pawan
Joe, When I put % in front of the user defined function, it started behaving like an inert function. E.g. if function f is defined, %f behaves as inert and value command can evaluate the function. Pawan
Edgardo, Thanks for your detailed reply to my message. I truly appreciate the hard work your team has put into introducing the indicial notation capabilities to the new Physics package. I am excited that among the major smps, Maple has taken lead and is far ahead of anyone else in including these capabilities in the package itself. The quality of your feedback and openly discussing the capabilities your team is planning to introduce in near future, makes it a really attractive platform. It is for this reason, that I have abandoned using one competitor package and decided to do all my symbolic manipulations in Maple. Now coming to your reply, let me clarify some points: 1) I mentioned about small and large indices from classical mechanics perspective. In many classical continuum mechanics textbooks, the smaller indices are used to denote the Eulerian framework(fixed to spatial coordinates) and capital indices are used to denote the Lagrangian (fixed to the deforming body) framework. For example, if one defines two Euclidean coordinate systems by X and Y, and wants to use smaller indices for X and capital indices for Y, what is the way of doing this? Even if I could use Greek letters for Y coordinates, and Latin letters for X coordinates, it would solve my purpose. So, basically I should be able to define two 3-D frameworks one using Latin indices and the second using Greek indices and be able to combine them in a single equation and vary the indices independently. Maybe there is already a way using the existing methods, but I could not find the method in help files. 2) I am glad you are planning to introduce more examples on indicial notation capabilities. I am going to spend some time on new DG pacakge as well to see how it could be combined with the capabilities of physics package. Thanks, for introducing this new package and replying to my post. Pawan Takhar Texas Tech
Hi Edgardo, Thanks for your reply. The above works only when the derivative is w.r.t. one type of coordinate system in a single equation. However, sometimes one need to mix the two types of derivatives(both Lagrangian and Eulerian) in the same equation. For example, if Y denotes Lagrangian coordinates and X denotes Eulerian coordinates. If one needs to prove the following identity: X[k],p*Y[p],l=KroneckerDelta[k,l] where comma (",p" and ",l") denotes derivatives. The first derivative is w.r.t. Lagrangian index, p and the second derivative is w.r.t. Eulerian index q. The above equation involve both types of derivatives in a single equation. This proof is a trivial task by hand. In Maple, one can only define X as a tensor, but if one defines both X and Y as tensors: >Define(X,Y); >eq:=d_[p](X[k](Y,t),[Y])*d_[l](Y[p](X,t),[X]); #Above line gives error that variables [Y] was already defined as names or indices. #If one doesn't define X and Y, and directly type the equation eq:=d_[p](X[k](Y,t),[Y])*d_[l](Y[p](X,t),[X]); Then, I do not get the error, but Simplify command cannot reduce eq to Kronecker delta. It is not a problem to substitute above term in equations by the Kronecker delta, but is it OK to type this equation without defining X and Y as tensors? Thanks, Pawan
Hi Edgardo, Thanks for your reply. The above works only when the derivative is w.r.t. one type of coordinate system in a single equation. However, sometimes one need to mix the two types of derivatives(both Lagrangian and Eulerian) in the same equation. For example, if Y denotes Lagrangian coordinates and X denotes Eulerian coordinates. If one needs to prove the following identity: X[k],p*Y[p],l=KroneckerDelta[k,l] where comma (",p" and ",l") denotes derivatives. The first derivative is w.r.t. Lagrangian index, p and the second derivative is w.r.t. Eulerian index q. The above equation involve both types of derivatives in a single equation. This proof is a trivial task by hand. In Maple, one can only define X as a tensor, but if one defines both X and Y as tensors: >Define(X,Y); >eq:=d_[p](X[k](Y,t),[Y])*d_[l](Y[p](X,t),[X]); #Above line gives error that variables [Y] was already defined as names or indices. #If one doesn't define X and Y, and directly type the equation eq:=d_[p](X[k](Y,t),[Y])*d_[l](Y[p](X,t),[X]); Then, I do not get the error, but Simplify command cannot reduce eq to Kronecker delta. It is not a problem to substitute above term in equations by the Kronecker delta, but is it OK to type this equation without defining X and Y as tensors? Thanks, Pawan
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