Motion of Particles under Pseudo-Deformation

Document Type: Original Scientific Paper

Author

M G Kashi Vidyapith Varanasi

Abstract

In this short article, we observe that the path of particle of mass $m$ moving along $\mathbf{r}= \mathbf{r}(t)$ under pseudo-force $\mathbf{A}(t)$, $t$ denotes the time, is given by $\mathbf{r}_d= \int(\frac{d\mathbf{r}}{dt} \mathbf{A}(t)) dt +\mathbf{c}$. We also observe that the effective force $\mathbf{F}_e$ on that particle due to pseudo-force $\mathbf{A}(t)$, is given by $ \mathbf{F}_e= \mathbf{F} \mathbf{A}(t)+ \mathbf{L} d\mathbf{A}(t)/dt$, where $\mathbf{F}= m\ d^2\mathbf{r}/dt^2 $ and $\mathbf{L}= m\ d\mathbf{r}/dt$. We have discussed stream lines under pseudo-force.

Keywords

Main Subjects


1. H‎. ‎Kiechle‎, ‎Theory of $K$-loops‎,‎ Lecture Notes in Mathematics‎, ‎1778‎, ‎Springer-Verlag‎, ‎Berlin‎, ‎2002‎.

2. R. Lal, Transversals in groups, J. Algebra 181 (1996) 70–81.

3. R. Lal, A. C. Yadav, Topological right gyrogroups and gyrotransversals, Comm. Algebra 41 (2013) 3559–3575.

4. A. C. Yadav, R. Lal, Smooth right quasigroup structures on 1-manifolds, J. Math. Sci. Univ. Tokyo 17 (2010) 313–321.