The Lagrangian for a mechanical system is L = a q?² + b q?, Where q is a generalized coordinate and a and b are constants. The equation of motion for this system is (A) q? = ?(b/a) q² (B) q? = (2b/a) q³ (C) q? = -(2b/a) q³ (D) q? = +(2b/a) q³ (E) q? = (b/a) q³
Added by Rosa H.
Close
Step 1
Step 1:** Apply Lagrange's equation to the given Lagrangian L = aq + bq': 9 = d/dt(dL/dq') - dL/dq ** Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 70 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) The Lagrangian for a system of one degree of freedom can be written as $$L-frac{m}{2}left(phi^{2} sin ^{2} omega t+q q e sin 2 omega t+q^{2} omega^{2} ight)$$ What is the corresponding Hamiltonian? Is it conserved? (b) Introduce a now coordinate defined by $$Q=q sin a t$$ Find the Lagrangian in terms of the new construction the corresponding Hamill Ionian. Is $H$ conserved?
Sri K.
The Lagrangian for a harmonic oscillator in the dimensionless form is L(x,ẋ) = 1/2 ẋ² - 1/2 ω²x². Find a solution of Euler-Lagrange equations which satisfies the following conditions: x(t = 0) = 0, x(t = T) = X, where ωT < π / 2. Calculate the value of the action S = ∫₀ᵀ L(x(t), ẋ(t))dt for this path if ω = 0.3, T = 1.9 and X = 4.2
Deepanshu K.
In this problem you will prove the equation of motion (9.34) for a rotating frame using the Lagrangian approach. As usual, the Lagrangian method is in many ways easier than the Newtonian (except that it calls for some slightly tricky vector gymnastics), but is perhaps less insightful. Let $\delta$ be a noninertial frame rotating with constant angular velocity $\boldsymbol{\Omega}$ relative to the inertial frame $\boldsymbol{\delta}_{\mathrm{o}}$. Let both frames have the same origin, $O=O^{\prime} .$ (a) Find the Lagrangian $\mathcal{L}=T-U$ in terms of the coordinates r and $\dot{\mathbf{r}}$ of $\delta$. [Remember that you must first evaluate $T$ in the inertial frame. In this connection, recall that $\mathbf{v}_{\mathbf{o}}=\mathbf{v}+\mathbf{\Omega} \times \mathbf{r} . \mathbf{J}(\mathbf{b})$ Show that the three Lagrange equations reproduce (9.34) precisely.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD