compute a determining equation for conjugate points from a two-parameter family of extremals - Maple Help

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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 n extremals, there must be 2n 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

withVariationalCalculus

ConjugateEquation,Convex,EulerLagrange,Jacobi,Weierstrass

(1)

ConjugateEquationAsint+Bcost,A,B,1,0,t,0

sint

(2)

The conjugate points to 0 are the zeros of this.

See Also

VariationalCalculus, VariationalCalculus[Jacobi]


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