On the linearization of the generalized Ermakov systems
نویسندگان
چکیده
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler–Ermakov systems belong into this category but others, more generic, systems are also included.
منابع مشابه
Generalized Hamiltonian Structures for Ermakov Systems
We construct Poisson structures for Ermakov systems, using the Er-makov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations...
متن کاملLinearization of M-LINC Systems Using GMP and Particle Swarm Optimization for Wireless Communications
In this paper, an efficient algorithm for the efficiency maximization of the multilevel linear amplification using nonlinear components (M-LINC) systems is proposed regarding the linearity of the system. In this algorithm, we use the generalized memory polynomial (GMP) to provide a behavioral model for the power amplifier (PA) and calculate the power spectral density (PSD) of the output signal ...
متن کاملOn the Lie Symmetries of a Class of Generalized Ermakov Systems
The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as Hamiltonian Ermakov system and exactly solved in closed form.
متن کاملLie Point Symmetries for Reduced Ermakov Systems
Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2, R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of ...
متن کاملOptimal Control of Nonlinear Multivariable Systems
This paper concerns a study on the optimal control for nonlinear systems. An appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. In this fashion, the nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002