Plotting potential of 2 bodies.

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SUMMARY

The discussion centers on plotting the pseudo potential of two bodies as outlined in the MIT lecture notes on dynamics. The user successfully plotted the gravitational potential using Maple but encountered challenges when incorporating the centrifugal force into the pseudo potential equation. The key insight is that the variable 'r' represents the diagonal distance from the origin to the point (x,y), forming a right triangle with the x and y coordinates. The user resolved the issue with guidance and achieved a satisfactory graph.

PREREQUISITES
  • Understanding of gravitational potential and pseudo potential concepts
  • Familiarity with Maple software for plotting
  • Knowledge of basic trigonometry and right triangles
  • Ability to interpret mathematical functions and equations
NEXT STEPS
  • Explore advanced plotting techniques in Maple for multi-variable functions
  • Study the derivation and application of centrifugal force in dynamics
  • Learn about the mathematical representation of potential fields in physics
  • Investigate the implications of right triangle properties in physics problems
USEFUL FOR

Students and professionals in aeronautics, astrophysics, and dynamics, particularly those involved in modeling gravitational interactions and potential fields.

kagestodder
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Hi everyone,

Im currently following an example of this paper: http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec18.pdf

And have reached a standstill on page 5. I am trying to plot the pseudo potential of the two bodies. I have succeded in plotting the gravitational potential in maple. But when i want to plot the pseudo potential i have to use the function (14). But on the added centrifugal force there's r, which i pressume is the position vector.

Im not really sure how to plot this since i now have 3 (x,y,r) variables instead of 2(x,y). r must be some sort of function of x and y, i think? If anyone has ever plottet the potential field i would love to know what to do now.

Regards
and thanks in advance.
 
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Hint: r is the "diagonal" distance running directly from the origin to the point (x,y). x is the "horizontal" distance from the origin. y is the "vertical" distance from the origin. x, y and r form the three sides of a right triangle. What famous Greek do you think of when you look at a right triangle? :wink:
 
Doh!

thanks :) Graph looks perfect now!
 

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