Selected Papers of Demetrios G. Magiros: Applied Mathematics, Nonlinear Mechanics, and Dynamical Systems Analysis

ISBN-13: 9789401088695 / Angielski / Miękka / 2014 / 518 str.

S. G. Tzafestas

Opis

The theory of nonlinear oscillations and stability of motion is a fundamental part of the study of numerous real world phenomena. These phenomena, particularly auto-oscillations of the first and second kind, capture, para- metric, subharmonic and ultraharmonic resonance, asymptotic behavior and orbits' stability, constitute the core of problems treated in "Nonlinear Mechanics", and their study is connected with the names of H. Poincare, A. M. Lyapunov, N. M. Krylov and N. N. Bogolyubov. Professor Demetrios Magiros, a widely known scientist in the theories of oscillations and nonlinear differential equations, has devoted his numerous works to this significant part of modern physical science. His scientific results can be classified in the following way: I) creation of methods of analysis of subharmonic resonances under the nonlinear effect, 2) determination and analysis of the main modes of nonlinear oscillations on the basis of infinite determinants, 3) analysis of problems of celestial mechanics, 4) classification of stability of solutions of dynamic systems concepts, 5) mathematical analogs of physical and social systems. He has developed new methods and solutions for a great number of difficult problems of nonlinear mechanics making a significant contri- bution to the theory and applications of the field. Urgency, depth of perception of the considered phenomena, and practi- cal directness are characteristics of his work.

Spis treści

I Applied Mathematics and Modelling.- 1. A class of nonautonomous differential equations reducible to autonomous ones by an exact method. Proc. Natl. Acad. Sci., V. 58, no. 2 (1967): 412–419 [31].- 2. Nonlinear differential equations with several general solutions. Proc. Acad. of Athens, V. 52 (1977): 221–229 [50]. Also: Ukr. Math. J., V. 30, no. 2 (1978): 238–241 (see p. 499).- 3. The general solutions of nonlinear differential equations as functions of their arbitary constants. Proc. Acad. of Athens, V. 52 (1977): 524–532 [51].- 4. Actual mathematical solutions of problems posed by reality, (I): a classical procedure. Proc. Acad. of Athens, V. 45 (1970): 179–187 [39].- 5. Actual mathematical solutions of problems posed by reality, (II): applications. Proc. Acad. of Athens, V. 46 (1971): 21–31 [40].- 6. Physical problems discussed mathematically. Bull. Soc. Math. Grèce, nouv. ser., t. 611, fasc. I. (1965): 143–156 [25].- 7. Diffraction by a semi-infinite screen with a rounded end (with Joseph B. Keller). Comm. Pure Appl. Math., V. 14, no. 3 (1961): 457–471 [16].- 8. On the linearization of nonlinear models of the phenomena, pt. I: linearization by exact methods. Proc. Acad. of Athens, V. 51 (1976): 659–668 [47].- 9. On the linearization of nonlinear models of the phenomena, pt. II: linearization by approximate methods. Proc. Acad. of Athens V. 51 (1976): 669–683 [48].- 10. Characteristic properties of linear and nonlinear systems. Proc. Acad. of Athens, V. 51 (1976): 907–935 [49].- 11. Mathematical models of physical and social systems. Genl. Electric Co., R.S.D., Philadelphia, 1980 [46b].- II Nonlinear Mechanics.- 1. Subharmonic Oscillations and Principal Modes.- 12. Subharmonics of any order in case of nonlinear restoring force, pt. I. Proc. Athens Acad. Sci., V. 32 (1957): 77–85 [6].- 13. Subharmonics of order one third in the case of cubic restoring force, pt. II. Proc. Athens Acad. Sci., V. 32 (1957): 101–108 [7].- 14. Remarks on a problem of subharmonics. Proc. Athens Acad. Sci., V. 32 (1957): 143–146 [8].- 15. On the singularities of a system of differential equations, where the time figures explicitly. Proc. Athens Acad. Sci., V. 32 (1957): 448–451 [9].- 16. Subharmonics of any order in nonlinear systems of one degree of freedom: application to subharmonics of order 1/3. Inf. and Control, V. 1, no. 3 (1958): 198–227 [10].- 17. On a problem of nonlinear mechanics. Inf. and Control, V. 2, no. 3 (1959): 297–309; Also Proc. Athens Acad. Sci., V. 34 (1959): 238–242 [11].- 18. A method for defining principal modes of nonlinear systems utilizing infinite determinants (I). Proc. Natl. Acad. Sci., U.S., V. 46, no. 12 (1960): 1608–1611 [14].- 19. A method for defining principal modes of nonlinear systems utilizing infinite determinants (II). Proc. Natl. Acad. Sci., U.S., V. 47, no. 6 (1961): 883–887 [15].- 20. Method for defining principal modes of nonlinear systems utilizing infinite determinants. J. Math. Phys., V. 2, no. 6 (1961): 869–875 [17].- 21. On the convergence of series related to principal modes of nonlinear systems. Proc. Acad. of Athens, V. 38 (1963): 33–36 [19].- 2. Celestial and Orbital Mechanics.- 22. The motion of a projectile around the earth under the influence of the earth’s gravitational attraction and a thrust. Proc. Athens Acad. Sci., V. 35 (1960): 96–103 [12].- 23. The Keplerian orbit of a projectile around the earth, after the thrust is suddenly removed. Proc. Athens Acad. Sci., V. 35 (1960): 191–202 [13].- 24. On the convergence of the solution of a special two-body problem. Proc. Acad. of Athens, V. 38 (1963): 36–39 [20].- 25. The impulsive force required to effectuate a new orbit through a given point in space. J. Franklin Inst., V. 276, no. 6 (1963): 475–489; Proc. XIVth Intl. Astron. Congress, Paris, 1963 [21].- 26. Motion in a Newtonian forced field modified by a general force, (I). J. Franklin Inst., V. 278, no. 6 (1964): 407–416; Proc. XVth Intl. Astron. Congress, Warsaw, 1964 [22].- 27. Motion in a Newtonian force field modified by a general force (II). J. Franklin Inst., V. 278 (1964): 349–355. XVIth Int. Astron. Congress, Athens, Greece (1965): [23].- 28. Motion in a Newtonian force field modified by a general force, (III). Application: the entry problem (with G. Reehl). XVIIth Intl. Astron. Congress, Madrid (1966): 149–154 [26].- 29. The entry problem (with G. Reehl), Proc. Acad. of Athens, V. 41 (1966): 246–251 [27].- III Dynamical Systems Analysis.- 1. Stability Analysis.- 30. On the stability definitions of dynamical systems. Proc. Natl. Acad. Sci. (U.S.), V. 53, no. 6 (1965): 1288–1294 [24].- 31. Stability concepts of dynamical systems. Inf. and Control, V. 9, no. 5 (1966): 531–548 [28].- 32. Attitude stability of a spherical satellite (with A. J. Dennison). J. Franklin Inst., V. 286, no. 3 (1968): 193–203; Bull. Amer. Phys. Soc., ser. 2, V. 12, no. 3 (1967): p. 288 (Abstract) [33].- 33. Stability concepts of solutions of differential equations with deviating arguments. Proc. Acad. of Athens, V. 46 (1971): 273–278 [42].- 34. Remarks on stability concepts of solutions of dynamical systems. Proc. Acad. of Athens, V. 49 (1974): 408–416 [44].- 35. Stability Concepts of dynamical systems. Philadelphia: Genl. Electric Co., R.S.D., 1980 [54].- 2. Precessional Phenomena.- 36. On a class of precessional phenomena and their stability in the sense of Liapunov, Poincaré and Lagrange. Proc. VIIIth Intl. Symp. on Space, Tech. Sci., Tokyo (1969): 1163–1170 [35].- 37. On the helicoid precession: its stability and an application to a re-entry problem (with G. Reehl.). Proc. XXth Intl. Astron. Congress, Buenos Aires, Argentina (1969): 491–496 [37].- 38. Orientation of the angular momentum vector of a space vehicle at the end of spin-up. Proc. XXIInd Intl. Astron. Congress, Brussels, Belgium, 1971 [41].- 39. The stability of a class of helicoid precessions in the sense of Liapunov and Poincaré. Proc. Acad. of Athens, V. 17 (1972): 102–110 [43].- 3. Separatrices of Dynamical Systems.- 40. On the separatrices of dynamical systems, Proc. Athens Acad. Sci., V. 54 (1979): 264–287 [52].- 41. Separatrices of dynamical systems. Proc. IXth Conf. on Nonlinear Oscillations, Kiev., 1981 (Yu.A. Mitropolsky, ed.), Ukrainian Acad. Sci. (Math. Inst.) Kiev. Naukova Dumka (1984): 280–287.- Appendix: Papers in Russian.- 42. Nonlinear differential equations with several general solutions, Ukr. Math. J., Ukrainian Acad. Sci., V. 30, no. 2 (1978): 238–241 [50b].- 43. Unification of stability concepts. Philadelphia: Genl. Electric Co., R.S.D., 1980, Math. Fizika, Ukrainian Acad. Sci., V. 33 (1983): 16–21 [53].- Biographical note of D.G. Magiros.- Complete chronological list of Magiros’ publications.- Magiros’ unpublished works.