Changing Origin in Physical Context: Mathematical Approach

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SUMMARY

The discussion focuses on the mathematical approach to changing the origin in a physical context, specifically using position vectors, constant vectors, and unit vectors. It clarifies that when shifting the origin in a Cartesian coordinate system, adjustments must be made to the coordinates of functions accordingly. For example, the equation y=3x at the original coordinates (x0, y0) transforms to y=3x+1 when the origin is moved to (x4, y3). The discussion also explores the manipulation of equations involving position vectors and their derivatives when changing the origin.

PREREQUISITES
  • Understanding of Cartesian coordinate systems
  • Familiarity with position vectors and their derivatives
  • Knowledge of vector operations, including cross products
  • Basic algebraic manipulation of equations
NEXT STEPS
  • Study vector transformations in physics
  • Learn about the implications of changing coordinate systems in analytical geometry
  • Explore the concept of frame of reference in physics
  • Investigate the use of unit vectors in directional analysis
USEFUL FOR

This discussion is beneficial for students and professionals in physics, mathematics, and engineering who are dealing with coordinate transformations and vector analysis in physical contexts.

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In a general situation, how do you change origin (mathematically speaking) in a physical context i.e. with position vectors, constant vectors, unit vectors to certain directions ... ?

I am a bit confused with the concept.
 
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If You have a Cartesian co-ord system of x, y, z with origin set at 0,0,0 then you need to add or subtract from the x, y, z of the function by the amount you are moving the origin.

Ie if y=3x at origin x0,y0 then at a new origin x4,y3 the function will be y+3=3x+4 or y=3x+1.
 
So if I have an equation x'=(x(cross)n)+a
where x is the position vector, x' time derivative, n unit constant, a constant, then I get changing by x->x+c:
(x+c)'=((x+c)(cross)(n+c))+(a+c)
is this what you meant?
 

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