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Hamiltonian mechanics is the feminine side of classical physics. Its masculine side is Lagrangian mechanics, formulated in terms of velocities (tangent vectors) rather than momenta (cotangent vectors). Lagrangian mechanics focusses on the difference of kinetic – potential energies; Hamiltonian mechanics focusses on their sum.
Richard Montgomery, reviewing a book by Stephanie Frank Singer and recalling lectures by Shing-Shen Chern
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https://ita.calameo.com/books/006381478eccc02ab83e8 DERIVATA della FUNZIONE COSENO IPERBOLICO - INSIEME di DERIVABILITA' - LIMITE del RAPPORTO INCREMENTALE - DIMOSTRAZIONI PASSO PASSO - LIMITE ESPONENZIALE NOTEVOLE - CALCOLI con COMMENTI - GRAFICI ESPLICATIVI Calcolo della Derivata di una Funzione Trascendente Funzione Coseno Iperbolico Definizione della Funzione Dominio Incremento della x Rapporto incrementale Dimostrazioni Calcoli Passo Passo Grafici https://www.youtube.com/user/enzoexposito http://www.enzoexposito.it/mobile/anal_infin_derivate.html https://www.slideshare.net/EnzoExposito1 https://twitter.com/enzoexposyto #math #maths #mathematics #calculus #functions #derivative #derivatives #limits #exponential #sine #cosine #tangent #cotangent #secant #cosecant #hyperbolic_sine #hyperbolic_cosine #hyperbolic_tangent #hyperbolicfunctions #hyperbolic_functions #analisi #coseno #coseno_iperbolico #derivate #limiti #primitiva #seno #seno_iperbolico #tangente #cotangente (presso World) https://www.instagram.com/p/CiS7ak1rzjT/?igshid=NGJjMDIxMWI=
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Someone needs to go back to Trigonometry.
Trig chart
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the cotangent bundle (differential forms) is the feminine side of calculus-on-manifolds; the tangent bundle (vector-fields) is the masculine side.
Shing-Shen Chern, via Richard Montgomery
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