representing vectors in different axesall

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 Representing vectors in different axes

All positions, velocities, momentums and accelerations are really relative positions, relative velocities, relative momentums and relative accelerations. However in common usuage we generally think of posi-tions, velocities, momentums and accelerations as relative to Earth unless explicitly stated. The usual approach to using vector analysis in dynamics is to start with a vector space of position vectors locatingpoint masses and inertial bodies. The derivatives of the position vectors then produce the velocities and momentums and their derivatives in turn accelerations, forces and moments. Positions, velocities, momentums and accelerations, forces and momentums are all vector quatities and in a sense share the samemathematical vector space as they share real physical space. Rotatations are different to translational displacements. Rotations are not vector quantities;2 the rotation of a body is generally done in sequence All positions, velocities, momentums and accelerations are really relative positions, relative velocities, relative momentums and relative accelerations. However in common usuage we generally think of posi-tions, velocities, momentums and accelerations as relative to Earth unless explicitly stated. The usual approach to using vector analysis in dynamics is to start with a vector space of position vectors locating point masses and inertial bodies. The derivatives of the position vectors then produce the velocities and momentums and their derivatives in turn accelerations, forces and moments. Positions, velocities, momentums and accelerations, forces and momentums are all vector quatities and in a sense share the same mathematical vector space as they share real physical space. Rotatations are different to translational displacements. Rotations are not vector quantities;2 the rotation of a body is generally done in sequence the fuselage due to fuel or cargo movement etc.. Note also that an axis can of course itself be regardedas a body or frame, and its origin a point. Consequently an axis may be refered to as both a point anda body.5 Thus the translational velocity of the c.g. of the vehicle relative to Earth axes E is denoted u_gE .