Coordinate transformation under rotation

AI Thread Summary
The discussion focuses on the mathematical derivation of coordinate transformations when a system is rotated around the Z-axis. The new coordinates are expressed as X' = xcos(θ) - Ysin(θ), Y' = Xsin(θ) + Ycos(θ), and Z' = Z, where θ is the angle of rotation. Participants are encouraged to refer to rotation matrices for a clearer understanding of how these transformations are derived. The conversation emphasizes the need to understand the rotation of basis vectors to grasp the underlying mathematics. A deeper exploration of rotation matrices is suggested for further clarity.
mkbh_10
Messages
217
Reaction score
0
If a system is rotated around Z axis then the new coordinates are X'= xcos() - Y sin(),

Y'= Xsin() + Ycos()

Z'= Z

How is this obtained ??

() --->theta , angle of rotation around Z axis .
 
Physics news on Phys.org
Simply look at rotating the basis vectors through an angle theta about the z-axis.
 
i am nt getting it , need to know the mathematical derivation
 
how to get that rotation matrix ??
 

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

I Transformations for isotropy in terms of math
Replies
1
Views
1K
A Rotation matrix and rotation of coordinate system
Replies
2
Views
2K
A Order of rotations due to torque in 3DOF in simulations
Replies
2
Views
1K
I Effect of Nearby Mountain on an Ideal Pendulum
Replies
1
Views
1K
B Thoughts about Galilean transformations
Replies
13
Views
2K
I Velocity transformation between frames rotating relative to one another
Replies
1
Views
2K
I Resolve moment of inertia at an angle
Replies
2
Views
2K
I Lagrangian mechanics - generalised coordinates question
Replies
4
Views
1K
Rotational Frame Transformations
Replies
14
Views
2K
Observation about the rotation of a disc
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top