Abstract
Galileo (Galileo Galilei (Pisa 1564- Arcetri 1642) was the father of Modern Science. Professor of Mathematics in the University of Pisa since 1589, he moved to Padova and back to Pisa in 1611. He conceived and stated the scientific method, and was equally gifted for experiment, theory and publication of the results. He also tried to measure the speed of light and built the first astronomical telescope, becoming the founder of modern Astronomy. His Sidereus Nuncius (1610) is also a literary masterpiece for its clear and very readable style. When he reported the discovery of the Pianeti Medicei (Jupiter’s moons) and of the sunspots he was suspected of heresy. The foundations of Mechanics are in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze, attinenti alla meccanica ed ai meccanismi locali, Leiden (1636). The book was published abroad because of the persecutions by the Church, whose teaching was contrary to any motion of the Earth. He avoided the stake thanks to his prudence and to good relations with the catholic hierarchy. He was a friend of Pope Urbano VIII Barberini. Nevertheless he was taken to trial, forced to retract and imprisoned for the rest of his life in Arcetri. Thereafter, life was very hard for scientists in Italy for quite a long time) contradicted all the ancient wisdom and doctrine when he established the principle of inertia, clearly stated the principle of Relativity and measured the acceleration of gravity and the circular motion around the year 1600.
In the mathematical formulation of the classical theory, we meet key concepts that are needed in its extensions (Relativity, Quantum Mechanics). Theoretical Physics is a large body of knowledge, yet it is deeply unitary. No doubt, it begins here.
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- 1.
Galileo Galilei (Pisa 1564- Arcetri 1642) was the father of Modern Science. Professor of Mathematics in the University of Pisa since 1589, he moved to Padova and back to Pisa in 1611. He conceived and stated the scientific method, and was equally gifted for experiment, theory and publication of the results. He also tried to measure the speed of light and built the first astronomical telescope, becoming the founder of modern Astronomy. His Sidereus Nuncius (1610) is also a literary masterpiece for its clear and very readable style. When he reported the discovery of the Pianeti Medicei (Jupiter’s moons) and of the sunspots he was suspected of heresy. The foundations of Mechanics are in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze, attinenti alla meccanica ed ai meccanismi locali, Leiden (1636). The book was published abroad because of the persecutions by the Church, whose teaching was contrary to any motion of the Earth. He avoided the stake thanks to his prudence and to good relations with the catholic hierarchy. He was a friend of Pope Urbano VIII Barberini. Nevertheless he was taken to trial, forced to retract and imprisoned for the rest of his life in Arcetri. Thereafter, life was very hard for scientists in Italy for quite a long time.
- 2.
Isaac Newton (Woolsthorpe 1642-London 1727) was a professor in Cambridge since 1669; then he had already invented Calculus, although his book De Methodis Serierum et Fluxionum was published in 1671. The basic work about Mechanics is entitled Philosophiae naturalis principia mathematica, Iussu societatis regiae, London (1687). He subsequently discovered the law of gravity, and made discoveries in Optics. He also invented the calculus of variations. Unlike Galileo, he was not persecuted, but highly honored in his own country, receiving prestigious commissions from the Government.
- 3.
Leonhard Euler (Basel, Switzerland 1707- S. Petersburg, Russia 1783) was probably the greatest mathematician of all times. He contributed to all fields of analysis, number theory and geometry. He also wrote the book Mechanica about his results on the equations of motion.
- 4.
As usual, we speak about one variable q for short, but the argument is intended for a set of s variables.
- 5.
We shall see that in Quantum Mechanics, this is no longer true.
- 6.
Adrien Marie Legendre (Paris 1752- Paris 1833) academic of Sciences and one of the great mathematicians of his age.
- 7.
This early Irish genius (Dublin 1805 - Dublin 1865), at the age of 22, went to Trinity College to explain his reformulation of Mechanics, and immediately got a chair. He continued for the rest of his life to produce high-level results; he also worked on the quaternions, which are essentially the spin matrices that we will discuss later on.
- 8.
This is popular in scientific literature, see e.g. John D. Jackson, “Classical Electrodynamics”, John Wiley and Sons (1962).
- 9.
Any other lagrangian that differs by a total derivative \(\frac{d F(\overrightarrow{r}, t)}{d t}\) is equivalent.
- 10.
L.D. Landau e E.M. Lif\(\breve{s}\)its, Mechanics (Pergamon Press) Chap. 7.
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Cini, M. (2018). Analytical Mechanics. In: Elements of Classical and Quantum Physics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-71330-4_2
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