Project 9 how to describe the attitude and motion of an airplane, a molecule, and other structures that can turn in 3D.
It's easy to understand how to specify the position of an object in 3D: we need to give the (x,y,z) coordinates. If the object is something large, we might choose to give the coordinates of the object's center of mass. But if we've only specified the coordinates of the center of mass, we know where the object is, but it's still free to spin around that center of mass in a variety of ways. To complete define the position and attitude of the object, we need to specify more information, and we need to agree on conventions for how that information is defined.
In engineering, a common method of describing how an object has rotated from some standard reference position involves the Euler angles. In navigation, the deviations of a plane's attitude from the reference position are called yaw, pitch and roll. In mathematics, rotations can be represented by quaternions, a generalization of complex numbers.
For this case study, we will concentrate on describing rotations in terms of a matrix. In turn, we will find that a given rotation can be analyze in terms of basic rotation matrices that represent rotation in three orthogonal reference directions.
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