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VariationalCalculus

  

Jacobi

  

compute and solve Jacobi's equation for conjugate points

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Jacobi(f, t, x(t), X(t), h, a)

Parameters

f

-

integrand to be tested

t

-

independent variable

x(t)

-

dependent function or list of functions

X(t)

-

expression for the extremal (found by solving the Euler-Lagrange equations)

h

-

name for the unknown function in Jacobi's equation

a

-

initial point (left end of the interval)

Description

• 

The Jacobi(f, t, x(t), X(t), h, a) command finds Jacobi's equation and tries to find solutions of Jacobi's equation, that is, conjugate points.

• 

The routine returns an expression sequence consisting of Jacobi's equation and any solutions found by dsolve.

  

If dsolve encounters a problem, an error message is returned.

  

If dsolve fails to find a solution, only Jacobi's equation is returned.

• 

If the solution of Jacobi's equation has a zero on the region of interest, the extremal is not optimal.

Examples

withVariationalCalculus

ConjugateEquation,Convex,EulerLagrange,Jacobi,Weierstrass

(1)

fⅆⅆtyt22+yt22

f:=12ⅆⅆtyt2+12yt2

(2)

Jacobif,t,yt,sint,h,0

ⅆ2ⅆt2ht+ht,ht=_C1sint

(3)

See Also

dsolve

VariationalCalculus

 


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