Return to Question

Suppose you have a rigid body and you have two local coordinate systems on the body at $P_1$ and $P_2$ and we can write a vector in the $P_2$ coordinate system using $P_1$ via the transformation $v_{p2} = R*v_{p1} + T$.

We know the instantaneous angular velocity of the object written with respect to $P_1$, how do we compute it with respect to $P_1$ ? Additionally how do we compute the orientation of the object WRT $P_2$ assuming we know its orientation WRT $P_1$ - in other words suppose we know euler angles $(\alpha, \beta, \gamma )$ to rotate the object into the reference frame $P_1$ from a coordinate system located at $P_1$ which is parallel to the global coordinate system. How can we get the orientation of the object(euler angles) at origin $P_2$?

Suppose you have a rigid body and you have two local coordinate systems on the body at $P_1$ and $P_2$ and we can write a vector in the $P_2$ coordinate system using $P_1$ via the transformation $v_{p2} = R*v_{p1} + T$.

We know the instantaneous angular velocity vector of the object written with respect to $P_1$, how do we compute the angular velocity vector respect to $P_2$? Additionally how do we compute the orientation of the object with respect to $P_2$ assuming we know its orientation with respect to $P_1$? In other words suppose we know euler angles $(\alpha, \beta, \gamma )$ to rotate the object into the reference frame $P_1$ from a coordinate system located at $P_1$ which is parallel to the global coordinate system and we want to know the euler angles to transform the coordinate system at $P_2$ parallel to the global coordinate system to orient the object the same as it is oriented in $P_1$.

If you only know the angular velocity and not the linear acceleration of a point on a body, can you predict the global orientation of the body with respect to another point?

Suppose you have a rigid body and you have two local coordinate systems on the body at $P_1$ and $P_2$ and we can write a vector in the $P_2$ coordinate system using $P_1$ via the transformation $v_{p2} = R*v_{p1} + T$.

We know the instantaneous angular velocity of the object written with respect to $P_1$, how do we compute it with respect to $P_1$ ? Additionally how do we compute the orientation of the object WRT $P_2$ assuming we know its orientation WRT $P_1$ - in other words suppose we know euler angles $(\alpha, \beta, \gamma )$ to rotate the object into the reference frame $P_1$ from a coordinate system located at $P_1$ which is parallel to the global coordinate system. How can we get the orientation of the object(euler angles) at origin $P_2$?