Register to reply

Differential operators in arbitrary coordinate systems?

Share this thread:
lordkelvin
#1
Nov10-12, 06:17 PM
P: 22
Hi, physics undergraduate here. I don't know much about differential geometry yet, but I'm curious about this idea:

Say I encounter a boundary value problem, and I'm not sure what coordinate system would be 'easiest' to solve the problem in. Is there some way to put the differential operator in terms of an unknown metric tensor, then impose some conditions stemming from the boundary values of the problem onto the arbitrary metric tensor in order to select some 'best' coordinate system?

Say I wanted to find the eigenmodes of a parralelogram-shaped drumhead. I'm basically curious if there is some way for me to have mathematics tell me I'd be best off using skew coordinates. Same thing with spherical coordinates on a round drumhead.
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Chestermiller
#2
Nov12-12, 08:22 PM
Mentor
Chestermiller's Avatar
P: 5,387
Often, it is best to choose a coordinate system such that the coordinates on the boundaries are constants. This makes it much easier to apply the boundary conditions.


Register to reply

Related Discussions
Div and curl operators in a left-handed coordinate system? General Math 0
Coordinate systems Calculus & Beyond Homework 6
Unitary operators preserve normalization in arbitrary basis Advanced Physics Homework 1
QM: Arbitrary operators and their eigenstates Advanced Physics Homework 14
Evaluate the commutator [d^2x/dx^2, x] by applying the operators to an arbitrary func Advanced Physics Homework 3