Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem’s strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particleon-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2, does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the

The constrained Lagrangian and constrained Hamiltonian equations of motion for a general nonrelativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner. The numerical integration of the constrained equations of motion are discussed. It is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes. As an example, the developed constrained methods are applied to the periodically driven inverted n-linked pendulum. It is demonstrated how the constrained methods leads to very efficient numerical algorithms. In the case of the n-linked pendulum the computational complexity using the constrained methods is O(n) compared to O(n³) using the conventional unconstrained approach.

Artificial Life is partly aimed at understanding the organisation and complexity of living processes. In this paper the concept of a historical process is discussed with the aim of providing a framework with which to approach diverse phenomena in organismic, ecological, and evolutionary contexts. A historical process is such, not because it is subject to contingencies, nor because it may be explained in historical terms, but because it presents a special relation between its dynamics and changes in its own conditions of realisation. Such processes may lead to durable spontaneous patterns and novelty. It is argued that such patterns can provide powerful explanatory tools and that Artificial Life simulation techniques are well fitted for their exploration. To different degrees of explicitness, the central theme of much of the work that currently goes under the rubric of Artificial Life (AL) is the understanding of processes that lead to innovations, transitions, and spontane...

Dedicated to Klaus Kirchgässner on the occasion of his 70th birthday Abstract. We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T 3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S 1 action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J 2-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J 2-Hamiltonian is a collective Hamiltonian of the T 3 momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J 2 effect as geometric phases. Key words: Kepler vector field, derivation of variables, orbits dynamics and phases 1.

This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlinear controller design, fusing the recently introduced Dynamic Surface Control and the Control Lyapunov Function method, is presented as the solution. Stability is analyzed using concepts from Singular Perturbation Theory. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations.

this paper but instead will show how a very simple electric field pattern can reproduce their most striking Fig. 1. The liquid helium film is supported by a solid substrate (shaded). In region 2 the electric field is E 0 0. (The x- and y-axes are drawn to very different scales.) 3/9 WILLIAMS features. Even if our suggestion turns out not to be the explanation of the BH experiments, the results of the calculation are interesting because they show that experiments intended to study layers of helium, liquid or solid, on insulating substrates should incorporate checks to ensure that results are not affected by static electric fields

We study orbits in simpli ed models of galaxies which consist of two components, a disk and a halo. The disk is idealized as razor-thin, though we present evidence that this simplifying assumption is not critical. We nd that the presence of the disk causes many more resonances than have been found in similar smooth potentials. Those resonances grow at relatively modest values of energy, overlap, and give rise to many stochastic orbits. A signi cant range of regular orbits remain and show smooth KAM curves, even though the discontinuous potential due to the razor-thin disk means that current versions of the KAM theorem do not apply.

doi:10.1088/0143-0807/31/5/006

Abstract. A fast packet of cold atoms is coupled into a magnetic guide and subsequently slowed down by reflection on a magnetic potential barrier (‘mirror’) moving along the guide. A detailed characterization of the resulting decelerated packet is performed. We show also how this technique can be used to generate a continuous and intense flux of slow, magnetically guided atoms. PACS. 32.80.Pj Optical cooling of atoms; trapping – 42.50.Vk Mechanical effects of light on atoms, molecules, electrons, and ions – 03.75.Be Atom and neutron optics 1