Questions tagged [lagrange]
The lagrange tag has no usage guidance.
15
questions
7
votes
1
answer
942
views
How does Legendre transformation in classical mechanics relate to Adrien-Marie Legendre?
I tried to look for the history of Legendre transformation, which transformed Lagrangian mechanics to Hamiltonian mechanics, usually formulated as
$$
\begin{cases}
p_i = \frac{\partial L}{\partial v_i}...
- 173
2
votes
1
answer
228
views
Where did Lagrange write his technique of resolvents for solving polynomials?
From Andrew Ellinor & Satyajit Mohanty's article on a technique for solving cubics:
Using Lagrange's resolvents, to solve the cubic, one has to first solve a quadratic. Given the general cubic, $$...
- 409
0
votes
0
answers
68
views
How did Newton, Lagrange, Hamilton and others ideate their mechanical formulations?
What exactly did Lagrange do, historically? This is very relevant but the accepted answer just does similar speculations based on contextual details that I have done. It was mentioned that part of ...
- 409
1
vote
1
answer
135
views
Book suggestions on Lagrangian and Hamiltonian mechanics?
What are some books that talk about the origins of Lagrangian and Hamiltonian mechanics? I would like to dig deeper into the fundamental approach and the fundamentals of action and its principles.
4
votes
0
answers
128
views
Lagrange's Theorem as he stated it
In Wikipedia, I found that Lagrange did not state Lagrange's Theorem in its general form. He stated
"If a Polynomial in $n$ variables has its variables permuted in all $n!$ ways, the number of ...
- 338
3
votes
0
answers
112
views
How did Ruffini manage to extend the methods of Lagrange in order to "prove" the insolvability of the general quintic equation?
Since Lagrange published his Reflections papers during the early 1770s — around 30 years before Ruffini took up and extended the subject — I was wondering if there were any results that were ...
- 1,516
0
votes
0
answers
84
views
Was Lagrange the first to have used generalized coordinates?
I was wondering if Lagrange was the first to use generalized coordinates as defined by their wikipedia article.
- 1,516
0
votes
1
answer
87
views
What are the direct predecessors of Lagrange's theory of quadratic forms?
I was reading Stillwell's Mathematics and its History, where Lagrange's theory of quadratic forms is synoptically presented, and I was wondering of what are the direct predecessors of the theory.
...
- 1,516
2
votes
0
answers
218
views
Where can I find Lagrange’s original equilateral triangular solution for arbitrary masses?
This answer to What kind of triangle is formed by three unequal masses in a circular restricted three body orbit? explains that
In the Newtonian limit, an equilateral 3-body solution exists for any ...
- 2,143
0
votes
2
answers
666
views
Does the word "God" appear regularly in the works of Joseph Lagrange?
In the Religious opinions section of the Wikipedia article on Laplace, there is an excerpt from Antommarchi's "The Last Moments of Napoleon", in which it is written that
the name of God appeared ...
- 1,516
0
votes
1
answer
70
views
What was Lagrange's contribution to the Knights Tour Problem?
Did Lagrange make any noteworthy contribution to the Knights Tour Problem?
- 1,516
0
votes
1
answer
150
views
Was Lagrange aware of Hamiltonian mechanics?
In the book "The Road to Reality", Penrose claims that Joseph Lagrange was aware of Hamiltonian mechanics. Is there any evidence that this statement is true?
- 1,516
8
votes
0
answers
293
views
What exactly was Lagrange's "grave mistake" with respect to rotating bodies under hydrostatic equilibrium?
A comment below What would be different about satellite orbits if Earth were prolate? Would we have Sun-synchronous and Molniya orbits? got me reading Wikipedia's Jacobi ellipsoid which begins:
...
- 2,143
26
votes
1
answer
4k
views
How was Lagrange appointed professor of mathematics so early?
It is well-known that in 1755 Lagrange was appointed Professor of Mathematics at the Royal Artillery School in Turin. He was 19. His work up until then involves correspondence with Euler. Was he ...
- 559
2
votes
0
answers
263
views
Why did Lagrange say that Cauchy should learn literature before mathematics?
From Bruno Belhoste's Augustin-Louis Cauchy — A Biography:
Even if we should doubt the remark Valson attributed to Lagrange, it is likely that he did advise Louis-François about to his son's ...
- 945