Quasi-integrals of even-dimensional linear differential systems with skew-symmetric coefficient matrices
N. A. Izobov, С. Е. Карпович, L. G. Krasnevskii, А. В. Липницкий · Differential Equations · 2008
For a linear nonstationary system with skew-symmetric continuously differentiable coefficient matrix of arbitrary even dimension, we construct its quasi-integrals and obtain effective coefficient estimates for their deviations from the corresponding integrals in the stationary case. For each trajectory of motion described by such a system and lying on the sphere of the corresponding radius, these estimates permit precisely indicating a domain on the sphere containing the trajectory on a nonsmall time interval. The estimates can also be used for expanding the multidimensional motion of a mechanical object into multicomponent elements of lower dimension.