Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

User Tools

Site Tools

Trace:
book:chap6:6.2_lagrange_formalism

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision		Previous revision
book:chap6:6.2_lagrange_formalism [2022/02/14 12:10] – created abrilbook:chap6:6.2_lagrange_formalism [2022/02/14 14:06] (current) – [6.2.2 Mathematical background: variational calculus] abril
Line 299: Line 299:
 [[#quest_variationalCalculus_soap-film |Problem 6.5]] extends the present discussion to situations [[#quest_variationalCalculus_soap-film |Problem 6.5]] extends the present discussion to situations
 where one minimizes the surface //area// of a soap film, rather than a feature of a one-dimensional object. where one minimizes the surface //area// of a soap film, rather than a feature of a one-dimensional object.
-[[book:chap6:6.7_Worked_problems #quest_variationalCalculus_sphere |Problem 6.14]] addresses extremal paths on a sphere.+[[book:chap6:6.7_Problems #quest_variationalCalculus_sphere |Problem 6.14]] addresses extremal paths on a sphere.
 Unless two points lie exactly on opposite sides of the sphere (like North and South pole) there are exactly two trajectories of extremal length. Unless two points lie exactly on opposite sides of the sphere (like North and South pole) there are exactly two trajectories of extremal length.
 One of them is the shortest trajectory. One of them is the shortest trajectory.
Line 463: Line 463:
 expressed in terms of the generalized coordinates $\mathbf q$ and their time derivatives $\dot{\boldsymbol q}$.\\ expressed in terms of the generalized coordinates $\mathbf q$ and their time derivatives $\dot{\boldsymbol q}$.\\
 **d)** Determine the EOM for the component $q_i$ of $\mathbf q$ by evaluating the //Euler-Lagrange equation// **d)** Determine the EOM for the component $q_i$ of $\mathbf q$ by evaluating the //Euler-Lagrange equation//
 +<wrap #eq_defEulerLagrangeEq></wrap>
 \begin{align} \begin{align}
-      \label{eq:defEulerLagrangeEq} 
       \frac{\mathrm{d}}{\mathrm{d} t} \; \frac{\partial \mathcal L}{\partial \dot q_i}       \frac{\mathrm{d}}{\mathrm{d} t} \; \frac{\partial \mathcal L}{\partial \dot q_i}
       = \frac{\partial \mathcal L}{\partial q_i} \tag{6.2.6}       = \frac{\partial \mathcal L}{\partial q_i} \tag{6.2.6}
book/chap6/6.2_lagrange_formalism.1644837058.txt.gz · Last modified: 2022/02/14 12:10 by abril