Register to reply

Calculate the distance between these two points (sphr. and cyl. coordinates)

by Tanegashima
Tags: coordinates, distance, points, sphr
Share this thread:
Tanegashima
#1
Nov20-11, 12:05 AM
P: 3
1. The problem statement, all variables and given/known data

Calculate the distance between these two points:

(3;π/2;−1) and (5;3π/2;5) (cylindrical coordinates)
(10;π/4;3π/4) and (5;π/6;7π/4) (spherical coordinates)


Do I need to put them in cartesian coordinates and continue the calc. or can I do with integrals?


2. Relevant equations

->dl = dr r + r d∅ ∅ + dz ^k

->dl = dr r + r dθ θ + r sin (∅) ∅


3. The attempt at a solution
Phys.Org News Partner Science news on Phys.org
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
SammyS
#2
Nov20-11, 01:11 AM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,800
Quote Quote by Tanegashima View Post
1. The problem statement, all variables and given/known data

Calculate the distance between these two points:

(3;π/2;−1) and (5;3π/2;5) (cylindrical coordinates)
(10;π/4;3π/4) and (5;π/6;7π/4) (spherical coordinates)


Do I need to put them in Cartesian coordinates and continue the calc. or can I do with integrals?


2. Relevant equations

->dl = dr r + r d∅ ∅ + dz ^k

->dl = dr r + r dθ θ + r sin (∅) ∅


3. The attempt at a solution
Hi Tanegashima. Welcome to PF.

It's likely easier in Cartesian coordinates . But for the first one, what is the distance from (3, π/2) to (5, 3π/2) in polar coordinates?
Tanegashima
#3
Nov20-11, 10:31 AM
P: 3
Thanks, but can anyone provide me with a sample in sph.c. or cyl.c.?


Re: (2, π)

SammyS
#4
Nov20-11, 03:39 PM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,800
Calculate the distance between these two points (sphr. and cyl. coordinates)

No. The distance from (3, π/2) to (5, 3π/2) is 8.

Therefore, the distance (horizontal) from (3, π/2, -1) to (5, 3π/2, -1) is 8 units.

Of course the distance from (5, 3π/2, -1) to (5, 3π/2, 5) is 6 units.

These two distances are perpendicular to each other.


Register to reply

Related Discussions
Calculate distance - accleration, time, distance Introductory Physics Homework 8
Shortest arc between two points in polar coordinates Differential Geometry 5
Distance between 2 points in spherical coordinates Calculus 5
Intersection coordinates are my points right? Introductory Physics Homework 2
Homogeneous points & coordinates Differential Geometry 5