Comment by Courage on Degrees of freedom of rolling coin
Please correct me if I'm wrong, if the coin doesn't slip, doesn't it reduce the degrees of freedom by 1, because the angle of rotation of the coin and the horizontal distance covered aren't...
View ArticleComment by Courage on Why the Lagrangian $L$ is KE - PE? Why not KE + PE!
It's not always "minimised", may be "extremized" would be a better word
View ArticleComment by Courage on Heisenberg EOM for $\langle x \rangle$ in momentum...
Note that $\hat p$ is an operator, you cannot use it like a variable
View ArticleComment by Courage on Virtual Work - Is the presentation in Cornelius Lanczos...
There are $n$ generalised coordinates because there are $n$ points, having an external force or not, doesn't make a difference
View ArticleComment by Courage on Einstein Summation Convention: One as Upper, One as Lower?
In the textbooks I've seen the form $A_i B^i$ is introduced after introducing contra and covariant components, but prior to this the $A_i B_i$ is usually used
View ArticleComment by Courage on The difference between the forms of the Euler-Lagrange...
@Kake_Fisk They mean the same, The scalar is the potential, Conservative forces obey the rule $\nabla \times F=0$ which implies that $F$ can be written as $F=-\nabla V$ , where $V$ is a potential which...
View ArticleComment by Courage on Question in Lagrangian formalism
Even though you are right, The E-L equations for both the coordinates are individually $0$ too, you are just doing $0+0$, also $F_i$ in your equations is a non conservative force
View ArticleComment by Courage on About time and time dilation
Worth reading Taylor and wheeler - spacetime physics, he treats both space and time with the dimension of meters, and completely ignores the constant $c$, reading this book should probably answer all...
View ArticleComment by Courage on The speed of light upon reflection
You could perfectly explain this considering light in its particle form, A photon is not reflected, A new photon is returned instead.
View ArticleComment by Courage on How we chose the height while calculating potential...
Potential Energy is not stored in the body, it is the property of the system.
View ArticleComment by Courage on Hamilton's principle and virtual work by constraint forces
-1, I don't see how this answers OP's question
View ArticleComment by Courage on Uncertainty Principle derivation confusion
Hint : calculate $b^2 - 4ac$ and apply Schwarz inequality
View ArticleComment by Courage on Why is the d'Alembert's Principle formulated in terms...
Possible duplicate: physics.stackexchange.com/q/81742
View ArticleComment by Courage on Can air make shadows?
When the particles in air have a greater concentration than light particles, what do you mean by this?
View ArticleAnswer by Courage for Parallel RLC circuit, how branching currents may each...
Total current is the vector sum of all currents$$I_T=I_R + (I_L + I_C)$$$I_L$ and $I_C$ are $180$ degrees out of phase at resonance, so the total current becomes$I_T=I_R...
View ArticleDeriving an equation for the mass of a pendulum (Follow up)?
Following this question: Deriving mass from simple pendulum which is summarized below Some mass $m$ is release from rest at a horizontal position. $m$ reaches the bottom of its path (so directly under...
View ArticleAnswer by Courage for Conserved vector field with a potential function
If a vector field is conservative, it means that the work done by is independent of the path taken,The Work done is:$$W=\int _a^b \vec{F}\cdot d\vec{r}$$if the path is a closed curve $C$ then$$W=\int_C...
View ArticleAnswer by Courage for Dilemma About Energy : Can You EXPLAIN?
In the first:The energy of the mass till it reaches the height of uncompressed length of the spring:$E_i=mg(h+l)$ where $h$ is the height of the mass dropped from the uncompressed length of the spring...
View ArticleCalculus of Variations - Virtual displacements
I am currently reading "The Variational Principles of Mechanics - Cornelius Lanczos", in which the author talks about the variation of a function $F(q_1, q_2, \dots q_n)$where $q_1, q_2, \dots q_n$ are...
View ArticleAnswer by Courage for Maths of elliptical orbits
You can use the orbiltal equation$$r=\frac{k}{1+\epsilon \cos\theta}$$where $(r,\theta)$ are the polar coordinates, $k$ is a constant and $\epsilon$ is the eccentricity So, $$\dot{r}=\frac{\epsilon k...
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