First Integral Of System Research Articles

ON THE NEW THEORY OF GEOSTATIONARY SATELLITE MOTION

Lagrange's equations for geostationary satellite motion in spherical coordinates connected with the Laplacian plane are considered. The first integral of system of equations has been found. The intermediate orbit of satellite has been constructed.

Local first integrals of differential systems and diffeomorphisms

In this paper using theory of linear operators and normal forms we generalize a result of Poincare [11] about the non-existence of local first integrals for systems of differential equations in a neighbourhood of a singular point. As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semiquasi-homogeneous systems. Moreover, for diffeomorphisms and periodic differential systems we give definitions of their first integrals, and generalize the previous results about systems of differential equations to diffeomorphisms in a neighbourhood of a fixed point and to periodic differential systems in a neighbourhood of a constant solution.

Polynomial first integrals of systems in the plane with center type linear part

Polynomial first integrals of systems in the plane with center type linear part

On the nonexistence of rational first integrals for systems of linear differential equations

We present a description of all systems of linear differential equations which do not admit any rational first integral.

On the possibility of obtaining any first integral of a Hamiltonian system via the Poisson theorem

From two conveniently chosen first integrals of a Hamiltonian system it is possible (by taking Poisson brackets), to obtain all the local first integrals of the system.

Conservation Laws for Undergraduates

Conservation laws for physical systems are produced as first integrals for systems of differential equations by an elementary method which is systematic and accessible to undergraduates. It is shown that all first integrals for the system ẋk(t) = fk(x1, ċċċ, xn, t) (k = 1, ċċċ, n) are solutions of a linear first-order partial differential equation. Hence, they can be found by well-known textbook methods. This method is applied to some mechanical problems. A new first integral for projectile motion is derived and discussed.