robert
April 19th, 2003, 4:42 PM
I am struggling with rotating coordinate systems in analytical mechanics. Consider a satellite orbiting the earth and attach a coordiate system to it such that
The coordinate orgin orbits the earth at the same radius and rotation rate W1 as the satellite and has its x axis radially outward and its y axis tangential in the direction of motion.
Now a 2nd satellite happens to be nearby and we want to express its motion relative to the 1st satellite. The equation of motion for this is
m a' = F - mAo - 2mW X v' - mW X W X r'
where F is the real force acting (gravity), Ao is the acceleration of the coord. origin (-W1*W1*R1) and -2mW X v' is the apparent Coriolis Force.
Which W (omega r/sec) goes in the formula for coriolis?
W of the orgin of the coordinate system or W of 2nd satellite?
Thanks,
Robert.
The coordinate orgin orbits the earth at the same radius and rotation rate W1 as the satellite and has its x axis radially outward and its y axis tangential in the direction of motion.
Now a 2nd satellite happens to be nearby and we want to express its motion relative to the 1st satellite. The equation of motion for this is
m a' = F - mAo - 2mW X v' - mW X W X r'
where F is the real force acting (gravity), Ao is the acceleration of the coord. origin (-W1*W1*R1) and -2mW X v' is the apparent Coriolis Force.
Which W (omega r/sec) goes in the formula for coriolis?
W of the orgin of the coordinate system or W of 2nd satellite?
Thanks,
Robert.