
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 13th, 2017, 04:02 AM  #1 
Member Joined: Apr 2017 From: India Posts: 49 Thanks: 0  Differential equations
While deriving the equation for transverse acceleration, I came across following problem: It is written that: transverse acceleration=(dr/dt)*(ds/dt)+(dr/dt)*(ds/dt)+ r(d^2(s)/dt^2) In the next step it is written that this is equal to: Transverse acceleration = 1/r {(r^2)(d^2 (s))/(dt^2) +2r(ds/dt)}.......How?? 
April 13th, 2017, 04:45 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,092 Thanks: 852 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
April 13th, 2017, 07:27 AM  #3 
Member Joined: Apr 2017 From: India Posts: 49 Thanks: 0 
Well, yes I have the same doubt and after that they have written that: Transverse acceleration= 1/r {d((r^2)ds/dt)/dt} 
April 13th, 2017, 08:41 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,092 Thanks: 852 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
April 13th, 2017, 05:25 PM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,770 Thanks: 627 Math Focus: Yet to find out. 
transverse acceleration $= \dfrac{dr}{dt}*\dfrac{ds}{dt} + \dfrac{dr}{dt}*\dfrac{ds}{dt} + r \dfrac{d^2(s)}{dt^2}$ Transverse acceleration = $\dfrac{1}{r} * \dfrac{(r^2) (d^2 (s))}{dt^2} +2r \dfrac{ds}{dt}$ Transverse acceleration= $\dfrac{1}{r} \dfrac{\dfrac{d((r^2)ds}{dt}}{dt}$ This is the exact sequence of steps provided in your text? 

Tags 
differential, equations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Differential Equations  hyperbola  Calculus  34  November 26th, 2016 05:49 AM 
Partial Differential Differential Equations  rishav.roy10  Differential Equations  0  August 21st, 2013 05:59 AM 
differential equations  skyhighmaths  Differential Equations  3  September 13th, 2011 08:55 AM 
Differential equations  jakeward123  Differential Equations  18  March 10th, 2011 08:56 AM 
Differential Equations  MathematicallyObtuse  Differential Equations  11  November 21st, 2010 12:57 PM 