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Semi-holonomic constraints look something like the following: $$f(\mathbf{q},t)=\sum_{i=1}^nf_i(\mathbf{q},t)\dot{q}_i+f_0(\mathbf{q},t)=0$$ with the requirement that $f(\mathbf{q},t)$ be integra...
What is semiholonomic is? Holonomic actually means two point can be expressed by a equation. Non-holonomic can be expressed but, not properly. Holonomic e.g. $r^2-a^2=0$ Non-holonomic e.g. $r^2-a...
It depends on what you want from your calendar. If you simply want a way to keep track of time, then you can base it on anything you like. The earth spinning on its axis, the moon orbiting the ea...
No. A calendar or, more generally, a time measurement system, can be based on anything. While human calendars have (generally) been based on: Day = One cycle of the Earth's rotation Month = On...
Is it plausible to desire a "universal" calendar applicable everywhere in our universe? Must calendars be based on solar systems (Must calendars be "relational")? It might be that the universe "...
There's not really a fundamental interpretation of the Lagrangian because the Lagrangian that describes the dynamics of a system isn't unique - more than one Lagrangian can yield the correct equati...
Lagrangian is no energy. It’s just the Lagrangian. It's perhaps more fundamental than energy in a certain sense. In general, you can think of it as a function that minimizes the action. That's the...
I know this is a bit late, but if you still haven't figured it out, here goes: Firstly, let the mass per unit area of the disk be $\sigma = \frac{m}{\pi R^2}$. Consider a small element of area $d...
Your mistake is that you did a second derivative of $L$, taking the derivative according to both degrees of freedom together. Instead you need to make a separate equation for each degree of freedom...
The method is correct. when you write $s=vt$, $s$ is the horizontal distance and $v$ is the horizontal component of the initial velocity (and it happens to be that the initial velocity has only ...
$$L'=\frac{m}{2}(a\dot{x}^2+2b\dot{x}{y}+c\dot{y}^2)-\frac{k}{2}(ax^2+2bxy+cy^2)$$where a, b, and c are arbitrary constants but subject to the condition that $b^2 − ac \ne 0$. What are the equat...
For an absolute beginner : If you don't have any idea of any theories than, I would suggest to study theories at first. Just practice beginner problems at first which contains no-calculus(It's OK ...
Magic.. :D The question was reopened but, showing closed instead of reopened (It should show last_activity according to code). question link
In my notes from University the reason a material can exhibit superconducting properties is at really low temperatures electrons form Cooper pairs of which the electrons of the Cooper pairs have lo...
Edit: While this specific case isn't reproducible, there is a broader problem. This section is sometimes not showing up for people with moderator privileges, on some communities, and I don't yet k...
Let's first remember how you check that you are at an extremum (minimum, maximum, saddle point) of a normal differentiable function. You do so by checking that the first derivative is zero (plus fu...
$L=T-U$ Here, $L$ is Lagrangian. T is kinetic energy. U is potential energy. But, what Lagrangian actually is? I know what Holonomic and non-holonomic is. But, I was thinking what the Lagrangian re...
How to derive the Lagrangian differential force? $$\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}})+\frac{\partial L}{\partial x}=0$$ I was trying to do something. $$L=T-U=\frac{1}{2} m\dot{x}^...
Why abilities don't show in every user page? Take a look at @Mithrandir's profile according to his profile he doesn't have any ability. But, I don't think that he doesn't have ability. I was checki...
$$\sum_i F_i \cdot \delta r_i$$ is virtual work when internal force is $0$. For that reason, $$\sum_i F_i \cdot \delta r_i = 0$$ Here internal force stands for what? When a object's displacement ...
We know that electrons always repel electrons. But, if somehow they collide, then what will happen? I found a related question of above one in Quora. An incoming electron can instead make them ...
Answering from the point of view of a particle physicist. Meaning we consider an event where and electron and proton approach each other in an initially free condition (not already bound). Electro...
I'm assuming that what's happening is that, for $t<t_0$, there's no gravitational field, then it's mysteriously instantaneously turned on at $t=t_0$. We can perform a Taylor expansion of $x$ ar...
While electrons have positive and protons have negative charge. They should collide and vanish, shouldn't they? No. They have other attributes than just being packets of charge. You have to cons...
Force is perpendicular to the surface. And, green color "rod" is parallel to the surface. So, $$F = N - mg\cos \theta=0$$ Reference
