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We present a theoretical problem of uniform motions, i.e. motions with constant magnitude of the velocity in central fields as a nonholonomic system of one particle with a nonlinear constraint. The concept of the article is in analogy with the recent paper [21]. The problem is analysed from the kinematic and dynamic point of view. The corresponding reduced equation of motion in the Newtonian central gravitational field is solved numerically. Appropriate trajectories for suitable initial conditions are presented. Symmetries and conservation laws are investigated using the concept of constrained Noetherian symmetry [9] and the corresponding constrained Noetherian conservation law. Isotachytonic version of the conservation law of mechanical energy is found as one of the corresponding constraint Noetherian conservation law of this nonholonomic system. 2010 Mathematics Subject Classification. Primary: 70F25, 70B05, 70H03, 70H33; Secondary: 70G45, 58Z05.Key words and phrases. Central field, nonholonomic mechanical systems, isotachytonic constraint, isotachytonic conservation law of angular momentum, reduced and deformed equations of motion, constraint symmetry, isotachytonic version of conservation law of mechanical energy.Both authors appreciate support of their departments.

The paper deals with the geometric concept of mechanical systems of N particles. The systems are modelled on the Cartesian product R ¢ X N and its first jet prolongation J 1 .R ¢ X N / h R ¢ T X N , where X is a 3-dimensional Riemannian manifold with a metric G. The kinetic energy T of the system of N-particles is interpreted by means of the weighted quadratic form x Q G associated with the weighted metric tensor G which arises from the original metric tensor G and the system of N particles m 1 ; : : : ; m N. A requirement for the kinetic energy of the system of N particles to be constant is regarded as a nonholonomic, so-called isokinetic constraint and it is defined as a fibered submanifold T of the jet space R ¢ T X N endowed with a certain distribution C called canonical distribution, which has the meaning of generalized admissible displacements of the system of particles subject to the isokinetic constraint. Vector generators of the canonical distribution are found.

Particular violin tones were played by a professional violin player in an anechoic room. The tones from the whole violin range, played nonvibrato using selected bowing techniques (naturale, sul ponticello, sul tasto) and dynamics of playing (p, mf, f), were recorded. The analysis based on the short-time Fourier transform was used to compute the time courses of amplitudes and frequencies of separated harmonics from the SPL recordings of the tones. The time characteristics of the time envelopes of the whole tone and his harmonics were calculated in the next step. For example, attack time, decay time, and relative starting time were studied. The influence of playing techniques, dynamics, and tone pitch on these time characteristics was described.

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