# Linked Questions

1answer
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2answers
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### Lagrange's equation implying Newton's 2nd law? [duplicate]

The typical first application of Lagrange's equation is showing that it implies Newton's law for a particle whose Lagrangian is $L=\frac{1}{2}mv^2-V(x)$. Plugging this Lagrangian into Lagrange's ...
0answers
169 views

### Partial derivative of $v$ w.r.t. $x$ in Lagrangian dynamics [duplicate]

In Lagrangian dynamics, when using the Lagrangian thus: $$\frac{d}{dt}(\frac{\partial \mathcal{L} }{\partial \dot{q_j}})- \frac{\partial \mathcal{L} }{\partial q_j} = 0$$ often we get terms such ...
0answers
69 views

### Partial derivatives in Lagrangian formalism [duplicate]

Suppose I have a function $f = xy$. A partial derivative of $f$ with respect to $x$ implies holding $y$ constant: $$\frac{\partial f}{\partial x} = y$$ Does this mean that in order to evaluate ...
0answers
50 views

### Definition of integral functional [duplicate]

I'm reading the section of Marion and Thornton devoted to basics on the Calculus of Variations, and came across this definition for the functional: $$J = \int f(y(x), y'(x);x) dx$$ implying that $f$ ...
0answers
38 views

### Question on basic tensorial calculus on field theory [duplicate]

Working on the Maxwell field as a gauge theory, at some point the following derivative comes up: $\frac{\partial(\partial_iA_0)}{\partial A_0}=0$ which must be, accordingly to the theory, zero. My ...
0answers
38 views

### Partial Differentiation without chain rule in Euler Lagrange Equations [duplicate]

The Euler-Lagrange equations for a bob attached to a spring are $$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial v} = \frac{\partial L}{\partial x}$$ But $v$ is a function of $x$. Is it ...
0answers
35 views

### Independence of position and velocity vector [duplicate]

Hi I am a mathematics student with an interest in Physics. In our Physics elective our prof. said if $\vec r$ denotes the position vector then the velocity vector $\vec v = \vec {\dot r}$ is ...
0answers
21 views

### Derivation of Equation of motion from Euler-Lagrange Equation [duplicate]

Hello I am new to Lagrange's dynamics and have some doubts regarding derivation of equation of motion given in a text : Deriving Equation of motion for a free body(no-external forces) ,in one ...
10answers
4k views

### Will a ball slide down a lumpy hill over the same path it rolls down the hill?

Suppose I have a lumpy hill. In a first experiment, the hill is frictionless and I let a ball slide down, starting from rest. I watch the path it takes (the time-independent trail it follows). ...

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