Calculus of Variations Dependent variables and constraints

  • I
  • Thread starter shedrick94
  • Start date
  • #1
30
0
If we have a function:

\begin{equation} f(x,x',y,y',t) \end{equation} and we are trying to minimise this subject to a constraint of
\begin{equation} g(x,x',y,y',t) \end{equation}

Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y.

Would we insert f(x,x',y,y',t)-Ag(x,x',y,y',t) into both equations, where A is a constant? Or would each equation require a different constant in front of the constraint term g(x,x',y,y',t)??
 

Answers and Replies

  • #2
963
213
and we are trying to minimise this subject to a constraint of.
g(x,x′,y,y′,t)​
(2)(2)g(x,x′,y,y′,t)\begin{equation} g(x,x',y,y',t) \end{equation}

Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y.
pl. give explicit eq of constraint -that will define the set of generalized coordinates.
 

Related Threads on Calculus of Variations Dependent variables and constraints

Replies
28
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
8
Views
5K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
561
Replies
4
Views
3K
Replies
4
Views
4K
Replies
2
Views
669
Replies
16
Views
172
Replies
3
Views
1K
Top