I Deriving maximum velocity in a rotated frame

AI Thread Summary
To derive the maximum velocity of a particle in a rotated uv plane, one should represent the particle's maximum velocity vector M from the origin to the point (A, B) in the Cartesian plane. By drawing perpendicular lines from point M to the u and v axes, the coordinates of vector M in the rotated frame can be determined. Knowing the angle between the x-axis and the u-axis is crucial for calculating the lengths of these perpendiculars. It's also important to note that the v coordinate of the vector may be negative in certain configurations. This approach will clarify how to express the particle's maximum velocity in the new coordinate system.
jumbo1985
Messages
19
Reaction score
1
rotate%20frame_zps6lbjzvxf.jpg

I have a particle that travels in the cartesian plane with the maximum velocity of A units along the x-axis and B units along the y-axis per unit of time.

How do I go about deriving the maximum velocity of my particle in the rotated uv plane? (the maximum distance the particle can along the u and the v axes in one unit of time)

Any tips greatly appreciated.
 
Mathematics news on Phys.org
Hi jumbo:

I suggest it might help if you add an arrow in the diagram to represent the vector M from the origin to point (x=A,y=B). Then draw perpendiculars from (A,B) to the axes u and v. If you know the angle between x-axis and u axis, you can calculate the length of the perpendiculars to the u axis and v axis which represent the M coordinates with respect to the v axis and u axis respectively.

Hope this helps.

Regards,
Buzz
 
Thanks Buzz Bloom.

Is this what you mean?

vel_max_zpsuvcup2vg.jpg


Where the length of A' is the maximum distance my particle can travel along the u-axis of the rotated frame in one unit of time. Similarly, the length of B'...
 
Last edited:
Hi jumbo:

I apologize for not expressing my thought more clearly.

You want to draw a line, call it L, from the origin to the point M. M will be on the vertical green line at the height B. L represents the vector corresponding to the maximum velocity of the particle you are describing.

Next draw lines from the point M perpendicular to the u and v axes. These lines will show the coordinates of the vector L in the (u,v) coordinate system. The resulting diagram should help you figure out how to calculate the u and v coordinates of the vector L.

By the way, for the particular example you have drawn, you may want to notice that the v coordinate of L is negative.

Hope this helps.

Regards,
Buzz
 
I think I got it. Thanks Buzz

vel_max_2_zpscfsvfczk.jpg
 
  • Like
Likes Buzz Bloom
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top