I Lagrange Equations of Motion for a particle in a vessel

5
0
Summary
I cant seem to get the correct equation of motion from the Lagrangian.
I start out by substituting rcos(Θ) and rsin(Θ) for x and y respectively. This gives me z=(b/2)r^2. The Lagrangian of this system is (1/2)m(rdot^2+r^2⋅Θdot^2+zdot^2)-mgz. (rdot and such is the time derivative of said variable). I then find the time derivative of z, giving me zdot=br⋅rdot and plug it into the Lagrangian giving me (1/2)m( rdot^2 + r^2⋅Θdot^2 + b^2r^2⋅rdot^2) - (1/2)mgbr^2. (plugged in regular z too). Finding the Lagrange equation of motion for 'r' gives me (ddot will be the second time derivative of said variable) 0= rddot(1+b^2r^2)-r⋅Θdot^2 + b^2⋅rdot^2⋅r + gbr . This is not correct though, the right answer has a negative term of b^2⋅rdot^2⋅r. Any help would be greatly appreciated.
Sorry about the notation, I have no idea how to put the equations into the computer.
 

Attachments

Last edited:

BvU

Science Advisor
Homework Helper
12,189
2,714
Welcome back in PF !

Lagrange equation of motion
The ##\mathcal L## you work out (*)
$$ (1/2)m( \dot r^2 + r^2\dot \theta^2 + b^2r^2\dot r^2) - (1/2)mgbr^2 $$
looks good to me. What is the Euler-Lagrange equation you then use ?


(*) I 'typed':
$$ (1/2)m( \dot r^2 + r^2\dot \theta^2 + b^2r^2\dot r^2) - (1/2)mgbr^2 $$
 

Want to reply to this thread?

"Lagrange Equations of Motion for a particle in a vessel" You must log in or register to reply here.

Related Threads for: Lagrange Equations of Motion for a particle in a vessel

Replies
4
Views
1K
Replies
8
Views
4K
Replies
9
Views
2K
  • Posted
Replies
1
Views
2K
Replies
1
Views
528
Replies
7
Views
8K
Replies
6
Views
3K
Replies
1
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top