o:28775 Optimal shape and first integrals for inverted compressed column en We study optimal shape of an inverted elastic column with concentrated force at the end and in the gravitational field. We generalize earlier results on this problem in two directions. First we prove a theorem on the bifurcation of nonlinear equilibrium equations for arbitrary cross-section column. Secondly we determine the cross-sectional area for the compressed column in the optimal way. Variational principle is constructed for the equations determining the optimal shape and two new first integrals are constructed that are used to check numerical integration. Next, we apply the Noether’s theorem and determine transformation groups that leave variational principle Gauge invariant. The classical Lagrange problem follows as a special case. Several numerical examples are presented. Keywords: optimal shape; Pontryagin’s principle; first integrals 1552099 10.3390/math8030334 1552101 2227-7390 2023-04-12T06:57:52.276Z 44 no 46 Enes Kačapor Državni univerzitet u Novom Pazaru 0000-0001-6658-051X Teodor Atanacković Državni univerzitet u Novom Pazaru person 0000-0002-8714-1388 Ćemal Dolićanin Državni univerziet u Novom Pazaru person 0000-0003-4830-1454 application/pdf 352437 https://phaidrabg.bg.ac.rs/o:28775 no yes 1 70 92000001 20A01 Mathematics MDPI 8 334 2020