Geodesic
A General Hamilton-Jacobi Equation and Associated Problem of Lagrange
Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 317-321

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It is well known [1] that the variational problem of minimizing 1 where F is positive homogeneous of degree one in (henceforth abbreviated to "plus-one" in ) leads to a Hamiltonian H{xi, pi} and corresponding Hamilton-Jacobi equation 2 
McKiernan, M. A. A General Hamilton-Jacobi Equation and Associated Problem of Lagrange. Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 317-321. doi: 10.4153/CMB-1965-022-1
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     author = {McKiernan, M. A.},
     title = {A {General} {Hamilton-Jacobi} {Equation} and {Associated} {Problem} of {Lagrange}},
     journal = {Canadian mathematical bulletin},
     pages = {317--321},
     year = {1965},
     volume = {8},
     number = {3},
     doi = {10.4153/CMB-1965-022-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-022-1/}
}
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