Question

3. Consider a system with $T = \frac{1}{2}(\dot{q}_1^2 + \dot{q}_2^2)$, $V = f(q_1 - q_2)$, where $f$ is yet unspecified. Choose a new set of generalized coordinates, $q_1$, $q_2$, to reduce the equations of motion to an integral involving $f$. Find $q_1(t)$, $q_2(t)$ for general initial conditions if $f(x) = x^2$. (Hint: Choose, say, $q_2$, so that $\frac{\partial \mathcal{L}(q_i, \dot{q}_i)}{\partial q_2} = 0$.)

Name: 3. Consider a system with T = (1)/(2)(q̇1^2 + q̇2^2), V = f(q1 - q2), where f is yet unspecified. Choose a new set of generalized coordinates, q1, q2, to reduce the equations of motion to an integral involving f. Find q1(t), q2(t) for general initial conditions if f(x) = x^2. (Hint: Choose, say, q2, so that (∂ℒ(qi, q̇i))/(∂ q2) = 0.)
Uploaded: 2023-06-08T04:30:58-08:00
Duration: 3 min 8 s
Channel: Adi S
Description: 3. Consider a system with T = (1)/(2)(q̇1^2 + q̇2^2), V = f(q1 - q2), where f is yet unspecified. Choose a new set of generalized coordinates, q1, q2, to reduce the equations of motion to an integral involving f. Find q1(t), q2(t) for general initial conditions if f(x) = x^2. (Hint: Choose, say, q2, so that (∂ℒ(qi, q̇i))/(∂ q2) = 0.)

          3. Consider a system with $T = \frac{1}{2}(\dot{q}_1^2 + \dot{q}_2^2)$, $V = f(q_1 - q_2)$, where $f$ is yet unspecified. Choose a new set of generalized coordinates, $q_1$, $q_2$, to reduce the equations of motion to an integral involving $f$. Find $q_1(t)$, $q_2(t)$ for general initial conditions if $f(x) = x^2$. (Hint: Choose, say, $q_2$, so that $\frac{\partial \mathcal{L}(q_i, \dot{q}_i)}{\partial q_2} = 0$.)

3. Consider a system with T = (1)/(2)(q̇1^2 + q̇2^2), V = f(q1 - q2), where f is yet unspecified. Choose a new set of generalized coordinates, q1, q2, to reduce the equations of motion to an integral involving f. Find q1(t), q2(t) for general initial conditions if f(x) = x^2. (Hint: Choose, say, q2, so that (∂ℒ(qi, q̇i))/(∂ q2) = 0.)

Added by Miriam S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

06/08/2023

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We need to choose a new set of generalized coordinates q1 and q2 to reduce the equations of motion to an integral involving f. Show more…

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3. Consider a system with T = (q? +q2), V = f(q -q2), where f is yet unspecified. Choose a new set of generalized coordinates, q1, q2, to reduce the equations of motion to an integral involving f. Find q,(t),q,(t) for general initial conditions if f (x) = x2. (Hint: Choose, say, q2, so that (qi, d = 0 .) 092