# On the use and abuse of Newton's second law for variable mass problems

@article{Plastino1992OnTU, title={On the use and abuse of Newton's second law for variable mass problems}, author={Angel Ricardo Plastino and Juan C. Muzzio}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1992}, volume={53}, pages={227-232} }

We clarify some misunderstandings currently found in the literature that arise from improper application of Newton's second law to variable mass problems. In the particular case of isotropic mass loss, for example, several authors introduce a force that actually does not exist.

## 67 Citations

Remarks on Newton’s second law for variable mass systems

- Physics, EducationEuropean Journal of Physics
- 2018

Misinterpretations of Newton’s second law for variable mass systems found in the literature are addressed. In particular, it is shown that Newton’s second law in the form F ⃗ = p ⃗ ˙ is valid for…

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Newton’s law of motion is derived from Kepler’s laws of planetary motion. This is achieved by applying a simple system identification method using numerical data from the planet’s orbits in…

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- Mathematics, Physics
- 1999

An appropriate generalization of the Jacobi equation of motion for the polar moment of inertia I is considered in order to study the N-body problem with variable masses. Two coupled ordinary…

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Newton’s law of motion is derived using Galileo’s experimental data from the inclined plane. This is achieved by developing a simple system identification method using measured distances and…

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- 2017

Departing from d’Alembert’s principle, the classical deductions of Hamilton’s principle and, from it, of Lagrange's equations, are extended to the case of discrete systems of variable mass. These…

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- Geology
- 2017

The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following…

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- 2019

We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of…

## References

SHOWING 1-10 OF 11 REFERENCES

Equations of motion of the restricted problem of three bodies with variable mass

- Mathematics, Physics
- 1983

In this paper we have deduced the differential equations of motion of the restricted problem of three bodies with decreasing mass, under the assumption that the mass of the satellite varies with…

The dynamics of bodies with variable masses

- Physics
- 1984

The Lie-series provide a convenient and simple method to solve systems of differential equations, especially in problems dealing with variable masses. A system of n-bodies moving isside a cloud and…

Does mass really depend on velocity, dad?

- Physics
- 1987

Relativistic mass is discussed in both a pedagogical and historical context. It is pointed out that its introduction into the theory of special relativity was much in the way of a historical…

Gravitational Physics of Stellar and Galactic Systems

- Physics
- 1985

Preface Introduction 1. Idealized homogeneous systems - basic ideas and gentle relaxation 2. Infnite inhomogeneous systems - galaxy clustering 3. Finite spherical systems - cluster of galaxies,…

Galactic mass loss - A mild evolutionary correction to the angular size test

- Physics
- 1982

Galactic mass due to gas production by an evolving stellar population and removal due to supernovae or some other energy source can alter the size of a galaxy over a long time through the adiabatic…

Trojan orbits with mass exchange of the primaries

- Physics
- 1984

The librational motion round the Lagrangian triangular points L4, L5 with mass exchange of the primaries is investigated according to Brown's theory. The results are the same as in the case of…