38
L. Cveticanin and D. Cveticanin
jump-like, while the position of the parts is assumed to be invariant during separation. Based on the principles of the linear and angular momentum, the equations
of motion for a body with continual mass variation are obtained. In the equations,
the reactive force, reactive torque and moment of the reactive force occur. Reactive
force and reactive torque are dynamic loadings which are evident only for those
bodies whose mass is varying in time. The body which has the oscillatory motion
and variable mass is considered. The one-degree-of-freedom oscillator is considered.
Mathematical model of the system is formed using the equations developed in the
paper. The equation is approximately solved using the Ateb functions. Two cases
are analyzed: The reactive force is taken into consideration, and then, the reactive
force is omitted. The results are quite opposite. It is concluded that in spite of the
fact that the mass variation is small and slow the reactive force has to be taken into
consideration. Otherwise, the obtained results are not correct.
Acknowledgements Investigation is supported by Faculty of Technical Sciences in Novi Sad (Proj.
No. 05/2019).
References
1. I.V. Meshcherskij, Rabotji po mehanike tel peremennoj massji (Gos. Izd. tehniko-teoret.lit,
Moscow, 1952)
2. A. Cayley, On a class of dynamical problems. Proc. R. Soc. London III, 506–511 (1857)
3. L. Ch. Dufour. Sur lacceleration seculaire du mouvement de la lune,Comptes rendus des Seances
de l’Ac. des Sc. LXII, 840–842 (1866)
4. A. Oppalzer, Ueber die Ursache, welche den Unterschied zwischen der theoretischen berechneten Secularacceleration in der Laenge des Mondes und der thatsaechlichen bedingen kann.
Astron. Nachr. 108(2573), 67–72 (1884)
5. H. Gylden, Die Bahnbewegungen in einem Systeme von zwei Koerpern in dem Falle das
Massen Veraenderungen unterworfen sind. Astron. Nachr. 109(2593), 1–6 (1884)
6. I.V. Meshcherski. Odin chasnij sluchaj zadachi Gouldena. Astronomische Nachrichten
132(3153), 9 (1893)
7. J. Fejoz. Quasiperiodic motions in the planar three-body problem. J. Diff. Equat. 183, 303–341
(2002)
8. J. Fiol, R.E. Olson. Three- and four-body dynamics in fast heavy ion atom ionization. J. Phys.
B At. Mol. Opt. Phys. 37, 3947–3960 (2004)
9. L. Cveticanin, Particle separation form a four particle system. Eur. J. Mech. A/Solids 26,
270–285 (2007)
10. J.E. Howard, Particle dynamics with variable mass and charge. Phys. Lett. Sect. A Gener. At.
Solid State Phys. 366(1–2), 91–96 (2007)
11. L. Cveticanin, D. Djukic, Dynamic properties of a body with discontinual mass variation.
Nonlinear Dyn 52(3), 249–261 (2008)
12. L. Cveticanin, Dynamics of Bodies with Time Variable Mass (Springer, Berlin, 2015)
13. I.V. Meshchersky, Dinamika tochki peremennoj massji (Peterburgski Universitet, Petersburg,
Magistarskaja disertacija, 1897)
14. L. Meirovitch, General motion of a variable-mass flexible rocket with internal flow. J. Spacecraft
Rockets 7(2), 186–195 (1970)
15. J.W. Cornelisse, H.F.R. Schoyer, K.F. Wakker, Rocket Propulsion and Space Fleight Dynamics
(Pitman, London, 1979)
L. Cveticanin and D. Cveticanin
jump-like, while the position of the parts is assumed to be invariant during separation. Based on the principles of the linear and angular momentum, the equations
of motion for a body with continual mass variation are obtained. In the equations,
the reactive force, reactive torque and moment of the reactive force occur. Reactive
force and reactive torque are dynamic loadings which are evident only for those
bodies whose mass is varying in time. The body which has the oscillatory motion
and variable mass is considered. The one-degree-of-freedom oscillator is considered.
Mathematical model of the system is formed using the equations developed in the
paper. The equation is approximately solved using the Ateb functions. Two cases
are analyzed: The reactive force is taken into consideration, and then, the reactive
force is omitted. The results are quite opposite. It is concluded that in spite of the
fact that the mass variation is small and slow the reactive force has to be taken into
consideration. Otherwise, the obtained results are not correct.
Acknowledgements Investigation is supported by Faculty of Technical Sciences in Novi Sad (Proj.
No. 05/2019).
References
1. I.V. Meshcherskij, Rabotji po mehanike tel peremennoj massji (Gos. Izd. tehniko-teoret.lit,
Moscow, 1952)
2. A. Cayley, On a class of dynamical problems. Proc. R. Soc. London III, 506–511 (1857)
3. L. Ch. Dufour. Sur lacceleration seculaire du mouvement de la lune,Comptes rendus des Seances
de l’Ac. des Sc. LXII, 840–842 (1866)
4. A. Oppalzer, Ueber die Ursache, welche den Unterschied zwischen der theoretischen berechneten Secularacceleration in der Laenge des Mondes und der thatsaechlichen bedingen kann.
Astron. Nachr. 108(2573), 67–72 (1884)
5. H. Gylden, Die Bahnbewegungen in einem Systeme von zwei Koerpern in dem Falle das
Massen Veraenderungen unterworfen sind. Astron. Nachr. 109(2593), 1–6 (1884)
6. I.V. Meshcherski. Odin chasnij sluchaj zadachi Gouldena. Astronomische Nachrichten
132(3153), 9 (1893)
7. J. Fejoz. Quasiperiodic motions in the planar three-body problem. J. Diff. Equat. 183, 303–341
(2002)
8. J. Fiol, R.E. Olson. Three- and four-body dynamics in fast heavy ion atom ionization. J. Phys.
B At. Mol. Opt. Phys. 37, 3947–3960 (2004)
9. L. Cveticanin, Particle separation form a four particle system. Eur. J. Mech. A/Solids 26,
270–285 (2007)
10. J.E. Howard, Particle dynamics with variable mass and charge. Phys. Lett. Sect. A Gener. At.
Solid State Phys. 366(1–2), 91–96 (2007)
11. L. Cveticanin, D. Djukic, Dynamic properties of a body with discontinual mass variation.
Nonlinear Dyn 52(3), 249–261 (2008)
12. L. Cveticanin, Dynamics of Bodies with Time Variable Mass (Springer, Berlin, 2015)
13. I.V. Meshchersky, Dinamika tochki peremennoj massji (Peterburgski Universitet, Petersburg,
Magistarskaja disertacija, 1897)
14. L. Meirovitch, General motion of a variable-mass flexible rocket with internal flow. J. Spacecraft
Rockets 7(2), 186–195 (1970)
15. J.W. Cornelisse, H.F.R. Schoyer, K.F. Wakker, Rocket Propulsion and Space Fleight Dynamics
(Pitman, London, 1979)