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VariationalCalculus[ConjugateEquation] - compute a determining equation for conjugate points from a two-parameter family of extremals
Calling Sequence
ConjugateEquation(extremals, parms, parm_values, t, t0)
Parameters
extremals
-
list of extremals, or algebraic expression for extremals
parms
list of parameter names
parm_values
list of parameter boundary values
t
independent variable
t0
one end point for the independent variable
Description
The ConjugateEquation(extremals, parms, parm_values, t, t0) command computes an algebraic equation. Its roots are the conjugate points.
The extremals option can be specified as a list, for example, [a*sin(t) + b*cos(t), c*sinh(t/c)+d*cosh(t/d)].
The extremals option can also be expressed algebraically, for example, A*cosh((t-a)/A).
If there are extremals, there must be parameters.
The parm_values options specifies the list of values of the parameters parms at the extremal points matching the boundary conditions of the problem.
The t0 option is an end point for the independent variable, for example, the left one.
To find any conjugate points, set the returned equation to 0 (zero) and solve.
Examples
The conjugate points to 0 are the zeros of this.
See Also
VariationalCalculus, VariationalCalculus[Jacobi]
Download Help Document
