A new approach to the equivalence problem (in phase space) is presented. Given a Hamiltonian describing a system of particles with two degrees of freedom (and the corresponding Hamilton–Jacobi equation), it is shown how to find the most general family of Hamiltonian functions that generates a new Hamilton–Jacobi equation with the following (and essential) characteristic, here defined as equivalence: Every new solution is also a solution of the original Hamilton–Jacobi equation and vice versa.

1.
D. G.
Currie
 and
E. J.
Saletan
,
J. Math. Phys.
7
,
967
(
1966
).
Google Scholar
Crossref
Search ADS
 
2.
Luiz J. Negri, “q‐Equivalências Generalizadas,” M. Sc. thesis, Universidade Federal da Paraíba, 1978.
3.
Y.
Gelman
 and
E. J.
Saletan
,
Nuovo Cimento B
,
18
,
53
(
1973
).
Google Scholar
Crossref
Search ADS
 
4.
Ian Sneddon, Elements of Partial Differential Equations (McGraw‐Hill, Kogakusha, 1957), Chap. 2, Sec. 9.
5.
A. R. Forsyth, A Treatise on Differential Equations (MacMillan, London, 1903), 3rd ed., Chap. IX, Sec. 200; see also Ref. 4,Chap. 2, Sec. 4.
This content is only available via PDF.
© 1986 American Institute of Physics.
1986
American Institute of Physics
You do not currently have access to this content.