Search results
Results From The WOW.Com Content Network
A non-autonomous system is a dynamic equation on a smooth fiber bundle over . For instance, this is the case of non-autonomous mechanics . An r -order differential equation on a fiber bundle Q → R {\displaystyle Q\to \mathbb {R} } is represented by a closed subbundle of a jet bundle J r Q {\displaystyle J^{r}Q} of Q → R {\displaystyle Q\to ...
A fundamental question is then how one can locate, out of this large family of invariant manifolds, the ones that have the highest influence on the overall system dynamics. These most influential invariant manifolds in the extended phase space of a non-autonomous dynamical systems are known as Lagrangian Coherent Structures. [4]
Non-autonomous mechanics describe non-relativistic mechanical systems subject to time-dependent transformations. In particular, this is the case of mechanical systems whose Lagrangians and Hamiltonians depend on the time.
In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems .
In mathematics, a non-autonomous system of ordinary differential equations is defined to be a dynamic equation on a smooth fiber bundle over .For instance, this is the case of non-relativistic non-autonomous mechanics, but not relativistic mechanics.
The stability of fixed points of a system of constant coefficient linear differential equations of first order can be analyzed using the eigenvalues of the corresponding matrix. An autonomous system ′ =, where x(t) ∈ R n and A is an n×n matrix with real entries, has a constant solution =
This is a list of dynamical system and differential equation topics, ... Examples of differential equations; Autonomous system (mathematics) ... a non-profit ...
Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.