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Can a quaternion be converted to an Euler angle?
These formulations are difficult to debug during implementation, require a different conversion method for each of the twelve Euler angle rotation sequences and provide little, if any, insight into the mathematical and geometric relationships among the entities.
When does bone formation and remodeling take place?
Modeling primarily takes place during a bone’s growth. However, in adult life, bone undergoes remodeling, in which resorption of old or damaged bone takes place on the same surface where osteoblasts lay new bone to replace that which is resorbed. Injury, exercise, and other activities lead to remodeling.
How are the shapes of bones related to each other?
Like other structure/function relationships in the body, their shapes and their functions are related such that each categorical shape of bone has a distinct function. Figure 6.2.1 – Classifications of Bones: Bones are classified according to their shape.
Where does bone development take place in the body?
region of bone development in the epiphyses zone of calcified matrix region of the epiphyseal plate closest to the diaphyseal end; functions to connect the epiphyseal plate to the diaphysis zone of maturation and hypertrophy
You can convert Euler angles to a quaternion and back to non-equivalent Euler angles. You can tell the second set of Euler angles gives a different rotation than the first because it converts to a different quaternion. For example: Thanks for contributing an answer to Mathematics Stack Exchange!
How is a rotation of an Euler angle represented?
A rotation of Euler angles is represented as a matrix of trigonometric functions of the angles. (2) Quaternions are an algebraic structure that extends the familiar concept of complex numbers.
How are Tait Bryan angles similar to Euler angles?
Similarly for Euler angles, we use the Tait Bryan angles (in terms of flight dynamics): where the X-axis points forward, Y-axis to the right and Z-axis downward with angles defined for clockwise/lefthand rotation.
How to calculate the rotation of a quaternion?
The quaternion is qy, β = cosβ 2 + (sinβ 2)j. Third, yaw around the world z axis. The quaternion is qz, γ = cosγ 2 + (sinγ 2)k. A rotation that is done in steps like this is modeled by multiplying the quaternions.