- #1
ManishR
- 88
- 0
consider object A with mass [tex]m_{A}[/tex]and inertial positional vector [tex]\overrightarrow{r_{A}}[/tex]
object B with mass [tex]m_{B}[/tex]and inertial positional vector [tex]\overrightarrow{r_{B}}[/tex]
object A with mass [tex]m_{C}[/tex]and inertial positional vector [tex]\overrightarrow{r_{C}}[/tex]
[tex]m_{A}\frac{d}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F}{}_{AB}+\overrightarrow{F}{}_{AC}[/tex]
[tex]\Rightarrow[/tex][tex]m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{B}}\right|^{3}}(\overrightarrow{r_{A}}-\overrightarrow{r_{B}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{C}}\right|^{3}}(\overrightarrow{r_{A}}-\overrightarrow{r_{B}})[/tex]
to get potential energy due to B and C, lhs and rhs need to be integrated with a non inertial positional vector. and i don't what that vector is.
please help
object B with mass [tex]m_{B}[/tex]and inertial positional vector [tex]\overrightarrow{r_{B}}[/tex]
object A with mass [tex]m_{C}[/tex]and inertial positional vector [tex]\overrightarrow{r_{C}}[/tex]
[tex]m_{A}\frac{d}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F}{}_{AB}+\overrightarrow{F}{}_{AC}[/tex]
[tex]\Rightarrow[/tex][tex]m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{B}}\right|^{3}}(\overrightarrow{r_{A}}-\overrightarrow{r_{B}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{C}}\right|^{3}}(\overrightarrow{r_{A}}-\overrightarrow{r_{B}})[/tex]
to get potential energy due to B and C, lhs and rhs need to be integrated with a non inertial positional vector. and i don't what that vector is.
please help