ένα άρθρο του Andrey Sakharov που γράφτηκε το 1968 για το περιοδικό Φυσική στη μέση εκπαίδευ-ση. Δημοσιεύθηκε το 1991 στο περιοδικό Κvant
από το περιοδικό Quantum, Τόμος 4 / Τεύχος 4 (Ιούλιος/Αύγουστος 1997)
ένα άρθρο του Andrey Sakharov που γράφτηκε το 1968 για το περιοδικό Φυσική στη μέση εκπαίδευ-ση. Δημοσιεύθηκε το 1991 στο περιοδικό Κvant
από το περιοδικό Quantum, Τόμος 4 / Τεύχος 4 (Ιούλιος/Αύγουστος 1997)
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
1) The document proves Bertrand's theorem, which states that the only central force laws that yield closed orbits for all bounded motions are the inverse-square law and Hooke's law.
2) It does this by starting with circular orbits and stable conditions, then considering orbits that slightly deviate from circular and requiring them to remain closed. This restricts forces to an inverse power law.
3) Considering larger deviations, it derives conditions on the power and finds only inverse-square and Hooke's laws satisfy the conditions to keep all orbits closed regardless of initial conditions.
This document provides an introduction to general relativity. It begins by summarizing the key aspects of special relativity, including that spacetime is four-dimensional and transformations between inertial frames form the Poincare group. It then discusses the equivalence principle and introduces curved coordinates to describe gravity. The document derives the affine connection and Riemann curvature tensor, and introduces the metric tensor. It provides the perturbative expansion leading to Einstein's field equations and discusses solutions like the Schwarzschild metric and gravitational radiation.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
1) The document proves Bertrand's theorem, which states that the only central force laws that yield closed orbits for all bounded motions are the inverse-square law and Hooke's law.
2) It does this by starting with circular orbits and stable conditions, then considering orbits that slightly deviate from circular and requiring them to remain closed. This restricts forces to an inverse power law.
3) Considering larger deviations, it derives conditions on the power and finds only inverse-square and Hooke's laws satisfy the conditions to keep all orbits closed regardless of initial conditions.
This document provides an introduction to general relativity. It begins by summarizing the key aspects of special relativity, including that spacetime is four-dimensional and transformations between inertial frames form the Poincare group. It then discusses the equivalence principle and introduces curved coordinates to describe gravity. The document derives the affine connection and Riemann curvature tensor, and introduces the metric tensor. It provides the perturbative expansion leading to Einstein's field equations and discusses solutions like the Schwarzschild metric and gravitational radiation.
