Advances in classical and analytical mechanics: A reviews of author’s results

Katica R. Hedrih-Stevanović

Theoretical and applied mechanics, Tome 40 (2013) no. 2, p. 293 .

Résumé

A review, in subjective choice, of author’s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author’s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelić and Rašković, as well as author’s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author’s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates.

Détail

DOI : 10.2298/TAM1302293H

Classification : 70E55 45L05
Keywords: Review, vector method, mass moment vectors, deviational mass moment vector, rotator, coupled rotations, no intersecting axes, basic vectors of position vector tangent space, angular velocity of the tangent space basic vectors, rheonomic constraint, rheonomic coordinate, mobility, angular velocity of basic vector rotation, velocity of basic vector extension, asymptotic approximation of solution, Krilov-Bogolyubov-Mitropolyski asymptotic averaged method, method of variation of constants, hereditary system, rheological and relaxational kernels, standard hereditary element, integro-differential equation, fractional order derivative, covariant coordinate, contravariant coordinate, Physical coordinate, discrete continuum method, space fractional order structure, chains, eigen main plane nets, eigen main chains, fractional order oscillator, fractional order properties characteristic number, transfer of signals, multi-frequency, material particles, rigid body, gyrorotor, deformable body, multi bdy system, transversal, longitudinal, multiplate system, multi-belt system, stochastic stability.