RT Journal Article
T1 On the polynomial first integrals of certain second‐order differential equations
A1 González Gascón, Francisco
A1 Ramos, F.B.
A1 Aguirre Dabán, Eduardo
AB It is shown that any first integral of type P2()—a polynomial of degree 2 in —of the differential equation =Vx can be obtained from a pointlike gauge symmetry of the action AL associated to L= 1/2 2+V(t,x). The same result holds for any first integral of kind Pn() when dynamical symmetries of AL polynomials in  are allowed. The neccessary and sufficient conditions that V(t,x) must satisfy in order that =Vx possesses a first integral of type Pn() have been obtained. These conditions reduce (when n=2) to a condition obtained by Leach. The computational advantages and difficulties which appear in order to obtain first integrals for type Pn() are also briefly discussed
PB American Institute of Physics
SN 1089-7658
YR 1982
FD 1982
LK https://hdl.handle.net/20.500.14352/64795
UL https://hdl.handle.net/20.500.14352/64795
DS Docta Complutense
RD 5 abr 2025