Parametric Equations Summary

discussionsummarypracticeproblems

Parametric Equations

Summary

  • N-dimensional motion can be completely described by n one-dimensional algebraic expressions along n mutually perpendicular directions (where n is any whole number greater than zero).
    • Two-dimensional motion can be completely described by two, one-dimensional algebraic expressions along two perpendicular directions.
    • Three-dimensional motion can be completely described by three, one-dimensional algebraic expressions along three mutually perpendicular directions.
r = x î + y ĵ + z k̂
v = vx î + vy ĵ + vz k̂
a = ax î + ay ĵ + az k̂
 
r2 = x2 + y2 + z2
v2 = vx2 + vy2 + vz2
a2 = ax2 + ay2 + az2
 
x = x(t) y = x(t) z = z(t)
  
x = Δx y = Δy z = Δz
Δt Δt Δt
x = Δvx y = Δvy z = Δvz
Δt Δt Δt
x = x(t)  y = x(t)  z = z(t) 
  
vx = dx vy = dy vz = dz
dt dt dt
ax = dvx = d2x ay = dvy = d2y az = dvz = d2z
dtdt2 dtdt2 dtdt2

Leave a Reply

Your email address will not be published. Required fields are marked *

*

This site uses Akismet to reduce spam. Learn how your comment data is processed.