Furthermore, Euler parameters, which allow a singularity-free description work of and dynamics 1 Euler In each body a translation One way a rigid way to angles [1]. R is the point r coordinate with space Since for Euler angles space. we use. Now let us assume that the space fixed coordinate system z it - ation of rotational motion, are discussed within the frame- quaternion algebra and are applied to the kinematics of a rigid body. Angles rigid body mechanics

we need to keep track of points for . The motion of such a body can be decomposed into and a rotation. Here we focus on the rotational part. to describe the rotation (the change in orientation) of body is by means of Euler angles. Or more precisely: a parametrize the rotation matrix is to use the three Euler For a rotation about a fixed origin, the rotation matrix orthogonal matrix which transforms the coordinates of a from the body fixed coordinate system to the space fixed system, as in r = Rr0; (1) fixed coordinates r and body fixed coordinates r0. a rigid body these body fixed coordinates are constant, is spanned by the three orthogonal unit vectors (~ex;~ey;~ez), also called the base vectors. To find the coordinates of the vector ~r expressed in the space fixed coordinate system we write,~r = x~ex +y~ey +z~ez. The coordinates are the three scalars x;y and and a handy way to describe them is to group them in a list. This list is then called the coordinate vector r = (x;y;z). Note the difference: the vector is~r whereas the coordinates of this vector expressed in some coordinate system are r. Eventually, if...

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