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VariationalCalculus[Jacobi] - compute and solve Jacobi's equation for conjugate points
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Calling Sequence
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Jacobi(f, t, x(t), X(t), h, a)
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Parameters
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f
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integrand to be tested
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t
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independent variable
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x(t)
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dependent function or list of functions
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X(t)
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expression for the extremal (found by solving the Euler-Lagrange equations)
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h
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name for the unknown function in Jacobi's equation
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a
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initial point (left end of the interval)
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Description
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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.
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The routine returns an expression sequence consisting of Jacobi's equation and any solutions found by dsolve.
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If dsolve encounters a problem, an error message is returned.
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If dsolve fails to find a solution, only Jacobi's equation is returned.
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If the solution of Jacobi's equation has a zero on the region of interest, the extremal is not optimal.
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Examples
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![[ConjugateEquation, Convex, EulerLagrange, Jacobi, Weierstrass]](/support/helpjp/helpview.aspx?si=9081/file03356/math122.png)
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