Go Back   Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Sep 26th 2008, 03:28 PM   #1
Junior Member
 
Join Date: May 2008
Posts: 12
inverted nonlinear pendulum, show unstable.

Hey there. I have a pendulum quandary.

Suppose we have a nonlinear pendulum. How can we show that the inverted

position is unstable?. And what is the exponential behavior of the angle in the

neighborhood of this unstable equilibrium position?.


I know the inverted position is at $\displaystyle {\theta}={\pi}$.

If even one initial condition causes the solution to tend away from equilibrium then it is unstable. But I do not know how to show that, much less explain the exponential behavior. I am thinking we can write the angle in terms of sine and cosine.

linearized stability analysis shows that if $\displaystyle f'(x_{E})<0$, then it is unstable. The displacement from equilibrium will grow exponentially for most initial conditions.

It would appear I need to take the derivative of some function using pi and show it is < 0. $\displaystyle sin(\pi)=0, \;\ cos(\pi)=-1$

Does anyone have any thoughts?. Thank you.
galactus is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Periodic and Circular Motion

Tags
inverted, nonlinear, pendulum, show, unstable



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Specific Heat of a nonlinear, temperature dependent spring Infernorage Advanced Thermodynamics 3 Sep 12th 2014 06:18 AM
Dog and Pony Show THERMO Spoken Here Kinematics and Dynamics 0 Sep 10th 2014 02:06 PM
Inverted pendulum roger Advanced Mechanics 2 Feb 21st 2013 11:59 AM
two coupled nonlinear equations abaset Theoretical Physics 0 Jul 28th 2012 01:12 AM
inverted wine bottle filled with water frend Thermodynamics and Fluid Mechanics 2 Jun 24th 2009 09:37 AM


Facebook Twitter Google+ RSS Feed