Question

particle P satisfy the differential equation
dr/dt = c x r show that P moves with a constant speed on a circular path
[ps. this is a math problem]

Answer 1

\[\Large \frac{d\mathbf{r}}{dt}=\mathbf{c}\times \mathbf{r}\] where c is a constant vector

Answer 2

I found a way to show that |v| is constant, but still no clue on showing that it is circular

Answer 3

\[\frac{\text{d}\mathbf{r}}{\text{d}t}=\mathbf{c}\times \mathbf{r}\]\[\mathbf{r}.\frac{\text{d}\mathbf{r}}{\text{d}t}=\mathbf{r}.(\mathbf{c}\times \mathbf{r})=0\]\[\mathbf{r}.\frac{\text{d}\mathbf{r}}{\text{d}t}=\frac{1}{2}\frac{\text{d}}{\text{d}t}(\mathbf{r}.\mathbf{r})=0 \ \ \Rightarrow |\mathbf{r}|=\text{const}\]------------------------------
\[\frac{\text{d}\mathbf{r}}{\text{d}t}=\mathbf{c}\times \mathbf{r}\]\[\mathbf{c}.\frac{\text{d}\mathbf{r}}{\text{d}t}=\mathbf{c}.(\mathbf{c}\times \mathbf{r})=0 \ \ \Rightarrow\]\[\mathbf{c}.\frac{\text{d}\mathbf{r}}{\text{d}t}=\frac{\text{d}}{\text{d}t}(\mathbf{c}.\mathbf{r})=0 \ \ \Rightarrow\]\[\mathbf{c}.\mathbf{r}=\text{const}\]\[|\mathbf{c}||\mathbf{r}|\cos \theta=a\]which is equation of a circle in spherial coordinates

Answer 4

I really want to save this for future reference, thanks mukushla you have been a great help