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Euler angle velocity (Definition)

The velocity of the Euler Angles of a rotating coordinate frame can be derived from the angular velocity vector of this frame with respect to a reference frame. The derivation is lengthy for each Euler angle sequence and is given in their respective entries. One useful result is acheived by combining the angular velocity vector, in terms of Euler angles, with Euler’s moment equations yielding the differential equations of motion that characterizes rigid body motion for a given sequence.

Notation: cos(𝜃) = c𝜃,sin(𝜃) = s𝜃

Euler angle velocity of 123 Sequence:

⌊ ϕ˙ ⌋ ⌈ 𝜃˙ ⌉ ψ˙ = ⌊ ⌋ (ωxc ψ − ωysψ)∕c𝜃 ⌈ ωxsψ + ωycψ ⌉ (− ωxcψ + ωysψ )s𝜃∕c𝜃 + ωz

Euler angle velocity of 321 Sequence:

⌊ ⌋ ϕ˙ ⌈ ˙ ⌉ 𝜃 ψ˙ = ⌊ ⌋ (ωys ψ + ωzc ψ)sec(𝜃) ⌈ ω c − ω s ⌉ y ψ z ψ ωx + ωys ψt𝜃 + ωzcψt𝜃


"Euler angle velocity" is owned by bloftin.
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Cross-references: Euler angle velocity of 321 Sequence, Euler angle velocity of 123 Sequence, rigid body, motion, differential equations, Euler's moment equations, Euler angle sequence, reference frame, vector, Euler Angles, velocity
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This is version 2 of Euler angle velocity, born on 2005-08-30, modified 2007-02-14.
Object id is 94, canonical name is EulerAngleVelocity.
Accessed 4746 times total.

Classification:
Physics Classification: 45.40.-f (Dynamics and kinematics of rigid bodies)
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