PDE constrained to a curve


by Sunfire
Tags: constrained, curve
Sunfire
Sunfire is offline
#1
Jul2-13, 10:31 AM
P: 177
Hello folks,

If we have the expression, say

[itex]\frac{∂f}{∂r}[/itex]+[itex]\frac{∂f}{∂θ}[/itex], am I allowed to change it to

[itex]\frac{df}{dr}[/itex]+[itex]\frac{df}{dr}[/itex][itex]\frac{dr}{dθ}[/itex],

if "f" is constrained to the curve r=r(θ).

My reasoning is that since the curve equation is known, then f does not really depend on the angle θ, but only on r (and r is a function of the angle, kind of a compound function).

Does this make sense?
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
Khashishi
Khashishi is offline
#2
Jul3-13, 05:52 PM
P: 832
This seems right conceptually, but notationally, some of those should be partial derivatives.
##\frac{\partial f}{\partial r} + \frac{\partial f}{\partial r} \frac{dr}{d\theta} = \frac{df}{dr}##
Sunfire
Sunfire is offline
#3
Jul3-13, 08:06 PM
P: 177
Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.


Register to reply

Related Discussions
constrained motion General Physics 1
a constrained sum Set Theory, Logic, Probability, Statistics 9
Constrained Maximization Calculus & Beyond Homework 3
Constrained Least Squares General Math 23
constrained PDE : 3D -> 1D Introductory Physics Homework 1