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bajaj562chpt7_2

# bajaj562chpt7_2 - 7.13 Eulerian Angles Rotational degrees...

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7.13 Eulerian Angles Rotational degrees of freedom for a rigid body - three rotations . If one were to use Lagrange’s equations to derive the equations for rotational motion - one needs three generalized coordinates . Nine direction cosines with six constraints given by are a possible choice . That will need the six constraint relations to be carried along in the formulation. Not the most convenient. [ ] [ ] [1] T ll 1

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One could use the angular velocity components to define the rotational kinetic energy . There do not exist three variables which specify the orientation of the body and whose time derivatives are the angular velocity components Need to search for a set of three coordinates which can define the orientation of a rigid body at every time instant ; z y x , , z y x , , 2
A set of three coordinates - Euler angles. • many choices exist in the definition of Euler angles - Aeronautical Engineering (Greenwood’s) y (right wing) x (forward) C C z (downward) x 3

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xyz system attached to the rigid body ; XYZ system is the fixed system attached to ground Two systems are initially coincident; a series of three rotations about the body axes, performed in a proper sequence, allows one to reach any desired orientation of the body (or xyz) w.r.t. XYZ .
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bajaj562chpt7_2 - 7.13 Eulerian Angles Rotational degrees...

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