Full range achieved, going from fastest to slowest works (downshift), but going from slowest to next slowest (upshift) fails. Limits are good, B-tension screw didn't help
- bicycles.stackexchange.com/questions/66811/rear-derailleur-does-not-downshift-properly-shifts-up-smoothly likely good question but with wrong up vs down terminology
Let's start with the one dimensional case. Let the and a Functional defined by a function of three variables :
Then, the Euler-Lagrange equation gives the maxima and minima of the that type of functional. Note that this type of functional is just one very specific type of functional amongst all possible functionals that one might come up with. However, it turns out to be enough to do most of physics, so we are happy with with it.
Given , the Euler-Lagrange equations are a system of ordinary differential equations constructed from that such that the solutions to that system are the maxima/minima.
By and we simply mean "the partial derivative of with respect to its second and third arguments". The notation is a bit confusing at first, but that's all it means.
Therefore, that expression ends up being at most a second order ordinary differential equation where is the unknown, since:
Now let's think about the multi-dimensional case. Instead of having , we now have . Think about the Lagrangian mechanics motivation of a double pendulum where for a given time we have two angles.
Let's do the 2-dimensional case then. In that case, is going to be a function of 5 variables rather than 3 as in the one dimensional case, and the functional looks like:
This time, the Euler-Lagrange equations are going to be a system of two ordinary differential equations on two unknown functions and of order up to 2 in both variables:At this point, notation is getting a bit clunky, so people will often condense the vectoror just omit the arguments of entirely:
Calculus of Variations ft. Flammable Maths by vcubingx (2020)
Source. And that is the whole point.
The outcome of that however is that you have to learn how to explain what you've achieved to others and why it is awesome.
Just like in the real world.
You have to create portfolio, and do some public relations.
en.wikipedia.org/wiki/The_Honourable_Schoolboy#Adaptations mentions:
Jonathan Powell, producer of Tinker, Tailor, Soldier, Spy (1979), said the BBC considered producing The Honourable Schoolboy but a production in South East Asia was considered prohibitively expensive and therefore the BBC instead adapted the third novel of the Karla Trilogy, Smiley's People (1979)
Refinement of the Bohr model that starts to take quantum angular momentum into account in order to explain missing lines that would have been otherwise observed TODO specific example of such line.
They are not observe because they would violate the conservation of angular momentum.
Introduces the azimuthal quantum number and magnetic quantum number.
There are unlisted articles, also show them or only show them.