Revista Tinerilor Economiºti (The Young Economists Journal)

Revista Tinerilor Economişti (The Young Economists Journal)
± sin 2Aθ
x = (19)
a
The differential equation (10) yields by direct computation
2
dy 2sin
Aθ
= (20)
dt a
and from (15) and (20) it follows
2A 2
dy = sin ( 2Aθ
) dθ
2
a
which yields
Aθ
sin( 4Aθ
)
y = − , (21)
2
2
a 4a
4. Conclusions
We have obtained the solution of a distributional system with degenerate cost
using the Hamilton’s equations on dual space and a convenient change of variables. The
novelty is to consider the degenerate cost of Kropina type as a deformation of the
quadratic cost.
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