Motion of Particles under Pseudo-Deformation

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 $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. 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} dmathbf{A}(t)/dt$, where $mathbf{F}= m d^2mathbf{r}/dt^2 $ and $mathbf{L}= m dmathbf{r}/dt$. We have discussed stream lines under pseudo-force.