Coriolis/centripetal force

X = 6x1 vector of end effector coordinates, k, k = 6x1 spatial vectors of end effector rates and accelerations, fi(x, x) = 6x1 vectOT of centripetal and Coriolis forces, and p(x) = 6x1 vectOT of gravity forces. 

Thus the acceleration in the rotating frame equals the siun of the net force per unit mass that would be present in an inertial system and the two apparent forces due to the rotation of the coordinate system. When Newton s law is expressed in a rotating coordinate system, the Coriolis and centripetal accelerations are seen as additional forces per unit mass. 

The geostrophic wind considers a balance between the horizontal pressure gradient and Coriolis forces. A less restrictive balance is one that includes the centripetal acceleration terms in the horizontal momentum equations. The balance that follows is not obtainable by a rigorous... 

The wind Fgr satisfying this equation is called the gradient wind. Although the flow is steady, it is curved and hence there is a centripetal acceleratioa This acceleration is measured by the term V /r and may be considered to define a centrifugal force per unit mass. Therefore, the gradient wind may be seen as a balance between centrifugal, Coriolis, and pressure gradierrt forces. 

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