In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are ...

Abstract This paper is a review, which focuses on our work, while including an analysis of many works other researchers in the field quaternionic regularization. The regular quaternion models celestial mechanics and astrodynamics Kustaanheimo-Stiefel (KS) variables Euler (Rodrigues-Hamilton) parameters are analyzed. These derived by methods based differential equations perturbed spatial two-bod...

As demonstrated by the success of James Gleick’s recent book [19871,there is considerable interest in the scientific community and among the general public in “chaos” and the “new science” which is supposed to accompany it. However, as usual, it is not easy to separate hyperbole from fact. In an attempt to do this, I will offer a precise definition of chaos in the context of differential equati...

We study the dynamics of three bodies located on a straight line for given finite speed gravity in case where masses external and their distances to central body are identical. It is shown that motion these unstable escape velocity higher than corresponding classical celestial mechanics.

A new efficient method is presented for the numerical computation of families of periodic orbits of systems with three or more degrees of freedom. This method is based on a well-known procedure using the variational equations as well as on unconstrained optimization techniques. This combination accelerates the convergence of previous schemes. The new composite method has been implemented here o...

The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Parti...

A fast and efficient numerical integration algorithm is presented for the problem of the secular evolution of the spin axis. Under the assumption that a celestial body rotates around its maximum moment of inertia, the equations of motion are reduced to the Hamiltonian form with a Lie-Poisson bracket. The integration method is based on the splitting of the Hamiltonian function and so it conserve...