Pfaffian systems of species one

On Birkhoff's Pfaffian Systems*

The Pfaffian systems to which this paper is devoted were defined and considered for the first time in 1920 by G. D. Birkhoff in the Chicago Colloquium lectures. Later he was led to a consideration of them in his memoirf Stability and the equations of dynamics and published in his bookj Dynamical Systems the demonstration of the important results he announced there. I shall set down later the pr...

Invariants of Pfaffian Systems 515

Pfaffian Hybrid Systems

It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o...

Pfaffian Systems of A-Hypergeometric Systems II - Holonomic Gradient Method

We give two efficient methods to derive Pfaffian systems for A-hypergeometric systems for the application to the holonomic gradient method for statistics. We utilize the Hilbert driven Buchberger algorithm and Macaulay type matrices in the two methods.

Optimal control for holonomic and Pfaffian nonholonomic systems

Holonomic and Pfaffian nonholonomic systems are dynamical systems whose generalized coordinates and velocities are subject to smooth constraints. These systems are usually described by second order differential equations of motion and algebraic equations of constraint. We present an optimal control formulation for these systems that utilizes the multiplier rule to append both the equations of m...