Physics Library
 An open source physics library
Encyclopedia | Forums | Docs | Random | Template Test |  
Login
create new user
Username:
Password:
forget your password?
Main Menu
Sections

Talkback

Downloads

Information
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(\theta) = c_{\theta}, sin(\theta) = s_{\theta} $

Euler angle velocity of 123 Sequence:

$\left[ \begin{array}{c} \dot{\phi} \ \dot{\theta} \ \dot{\psi} \end{array} ... ...i} + \omega_y s_{\psi}) s_{\theta} / c_{\theta} + \omega_z \end{array} \right] $

Euler angle velocity of 321 Sequence:

$\left[ \begin{array}{c} \dot{\phi} \ \dot{\theta} \ \dot{\psi} \end{array} ... ...omega_y s_{\psi} t_{\theta} + \omega_z c_{\psi} t_{\theta} \end{array} \right] $



"Euler angle velocity" is owned by bloftin.

View style:


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, velocity
There are 2 references to this object.

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 3390 times total.

Classification:
Physics Classification45.40.-f (Dynamics and kinematics of rigid bodies)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:

No messages.

Testing some escape charachters for html category with a generator has an injective cogenerator" now escape ” with "