
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 31st, 2018, 09:04 AM  #1 
Newbie Joined: Jan 2018 From: iceland Posts: 2 Thanks: 0  Ellipsoid problem...c axis calculation
Hi all, i'm new on this forum. First of all sorry for my written english. I'm a PhD student in Earth Science and i need help with a geometry problem. I'm trying to determine the c axis of some ellipsoidshape objects. With the microscope I've measured the two axis in the xy plane and the length that i get when i rotate the object of 45°. I need to calculate the other axis in order to determine the thickness of these objects. I think that my case could be represented by this picture: https://www.researchgate.net/profile...dependent.png My Idea was to apply some trigonometry equations, as: Cos45 = measured length when rotated of 45° / c axis, and than get the c axis. Anyway i don't really like the result that i get, so i think i'm doing something wrong. Can you help me? any advice? Hope you understand the problem Thank you Alberto 
February 3rd, 2018, 03:59 AM  #2 
Newbie Joined: Jan 2018 From: iceland Posts: 2 Thanks: 0 
Nobody can help me? Cheers 
February 3rd, 2018, 09:50 AM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 535 Thanks: 306 Math Focus: Dynamical systems, analytic function theory, numerics 
You haven't said what a "c axis" is. However, if I'm understanding your question correctly you are interested in the coordinates for an ellipse after rotating it in the plane? The polar transformation for an ellipse gives the coordinates: $x = A \cos (\theta)$ and $y = B \sin(\theta)$ where $A,B$ are constants related to the eccentricity of the ellipse. If you write them in this way, then applying a rotation by $\alpha$ is nothing more than multiplication by the matrix \[ \left( \begin{array}{cc} \cos(\alpha) & \sin(\alpha) \\ \sin(\alpha) & \cos(\alpha) \end{array} \right) \] which can be combined with the polar coordinates for $x,y$ using standard trig identities. If this doesn't help, then you need to clarify what exactly you are asking. 

Tags 
axis, calculation, ellipsoid, problemc 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
angles between axis and rotation problem  Apollonio  Trigonometry  1  February 16th, 2016 02:50 AM 
x axis and y axis Product of slopes is equal to 1  brhum  PreCalculus  4  November 27th, 2014 05:16 AM 
Volume of ellipsoid  PedroMinsk  Calculus  5  December 3rd, 2010 01:14 PM 
Ellipsoid  lgavish  Real Analysis  1  June 29th, 2009 09:20 AM 
Area of ellipsoid  priyapathak  Algebra  1  January 16th, 2009 12:58 AM 