All Questions
22
questions
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2
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63
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Extending the Lagrangian of a double pendulum to systems with more complex shapes
The total kinetic energy of a double pendulum can be calculated as follows:
$$L = \frac{1}{2} (m_1 + m_2) {l_1}^2 \dot{\theta_1}^2 + \frac{1}{2} m_2 {l_2}^2 \dot{\theta_2}^2 + m_2 l_1 l_2 \dot{\...
1
vote
3
answers
65
views
Oscillating inverted hemisphere Lagrangian mechanics problem
I am trying to solve a hw problem on Lagrangian mechanics. Here is the problem:
The main issue I am having is setting up the kinetic energy. I don't understand whether the hemisphere has both ...
- 11
0
votes
1
answer
55
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Why is gravitational potential energy negative in this Lagrangian? [closed]
The question is given as follows:
From (6.109) shouldn't the Lagrangian be K(kinetic) - U(potential), but here its K + U? Unless the potential energy is negative, if so I'm struggling to come to ...
1
vote
1
answer
986
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Kinetic energy of double pendulum
using cartesian coordinates as an intermediate step, the kinetic energy is calculated as such
why is it incorrect to just say that the kinetic energy for the first bob is $$T_1 = (1/2) m_1 (l_1\dot{\...
- 460
0
votes
1
answer
149
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Problem 6.3 from David Morin (classical mechanics) [closed]
I get the lagrangian for the system as
$$
\begin{align}
\mathscr{L} = \frac{m}{2}(\dot{x}^2 + l^2\dot{\theta}^2 + 2l\dot{x}\dot{\theta}\cos \theta) + mgl\cos\theta
\end{align}
$$
Where $\theta$ is the ...
- 23
0
votes
2
answers
176
views
Lagrangian of inverted physical pendulum with oscillating base
An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
1
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0
answers
408
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Lagrange Equation for a physical pendulum attached to a spring
I have a very specific problem and need a lagrangian equation and differential equation for the motion of mass $m$.
The center of a metal rod with length $2R$ is attached to a ball bearing so it can ...
- 163
1
vote
1
answer
88
views
Energy of a system executing forced oscillations
In L&L's textbook of Mechanics (Vol. 1 of the Course in Theoretical Physics) $\S 22$ Forced oscillations, one finds the following statement:
\begin{equation}
\xi = \dot{x} + i \omega x, \tag{22.9}...
- 39
0
votes
2
answers
462
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Lagrangian of an elastic pendulum
I'm trying to understand the way my teacher found the Lagrangian of an elastic pendulum.
Given a spring pendulum connected to the origin, the equilibrium point is $(0,0,\frac{-mg}{k})$.
The length of ...
- 449
0
votes
2
answers
122
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Equilibrium positions of a tilted rod rotating around vertical axis
First of all, this is my first ever question on any forum so forgive me if it's not so well written. Second, I'm not a native English speaker so if there is any writing error, I'm sorry.
The problem ...
0
votes
1
answer
660
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Trouble finding the matrix form of potential energy in small oscillations (Goldstein linear triatomic molecule example)
I'm currently trying to learn small oscillations, I kind of comprehend the general theory, but I'm having hard times finding the matrix forms of the potential and kinetic energy. I have been following ...
- 7
0
votes
1
answer
148
views
Equations of the spherical pendulum in different coordinates [closed]
I am trying to derive the equations of motion of a spherical pendulum, but instead of using the angles of the spherical coordinate system $\theta$ and $\varphi$, I want to use the angles $\alpha$ and $...
- 197
0
votes
1
answer
146
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Lagrangian for nonlinear small oscillations
My original Lagrangian is this, but I want to obtain nonlinear terms considering small oscillations : $$ L = ma^2[\dot \theta^2(1+ 2\sin^2\theta) + \Omega^2\sin^2\theta + 2\Omega_0\cos\theta] . $$
...
0
votes
3
answers
960
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Expression for total potential energy in coupled systems
I was reading through applications of Lagrangian mechanics and the case of coupled oscillators. The example provided is the famous two pendula length $l$ mass $m$ hanging from the ceiling connected by ...
- 418
0
votes
3
answers
4k
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Lagrangian of an inverted pendulum on a moving cart
So I have been trying to derive the equations of motion of the inverted physical pendulum in a cart, but I seem to be confused about the derivation of its Kinetic Energy. I know this physical system ...
