[br]Neste trabalho buscou-se parametrizar, em coordenadas polares, a equação que descreve o decaimento de uma gota ao encontrar uma superfície. A equação inicial é dada por [br][br][img width=236,height=44]https://lh3.googleusercontent.com/qYZdeThHNos92kxiZk7Z_8TacdI_xumIvlgtig5mpUXS_LJRw54OBOOAnli5XlgJirf58TUognu61BBt6w7ZS664yEygRltWvXJb_s_mBTqY5vSiP5Ewb7AfkcD7BZSTp9EdDUubGj1aeV-YMqK_IlQ[/img][br][br]Parametrizando em função de [img width=8,height=7]https://lh3.googleusercontent.com/AOwN-1LBTLMKuBmjqRiOaTTa_qv358tBzf5apZB8rvjURoeslKXE9TqTQFb1tlCzorLuIC1wNoRxCLMJdnTqV3XDvwIWSbm5y0PQiHKK1CRE9BIl4RFnPTyRMpptSC2SRx6vZwsND_GQp7tHWJEecd4[/img] e [img width=7,height=7]https://lh4.googleusercontent.com/Q_6cKAT1PW0QVmG_uvRSNO9j14FsbIC-M-LglVngnpWiEm9X9P-iJZFahO2ZCAOnLlZKMiB1jlWOHqLxJcp1Qv9cDtqtxmQrDoG7llz01MjNoL6srB60hUhhCg-TEx7j76cFZEwVx0ceTb18BhRcuwY[/img] para as coordenadas polares, temos que [img width=105,height=16]https://lh3.googleusercontent.com/NJvkGanl3NqsAgaJqHI3N360f9abLqt5tpHmky-WjQxCaJrlwjUZMvNKrTTRzjFlcNWKjFqNqt48ceQ52kulCzJrBVzGnpyCgEbzPRO5RdsLwhxQPgQIuDb1ktagjbMkQu2OEGK73dnzKI7pgnC9mhs[/img], [img width=104,height=16]https://lh5.googleusercontent.com/JO6iWPCc-ynARi9BWZpQ2YZgNqPUSqYpaDvQaoDLy2CeNW9wGe2zuuQVE9ZwaIo4x4xFSvkjTB7WXuwRKdi59bkxixf7DtVAVdb0dsUTfWHwtiRIcXsgghZOKRCNnv-RYygDHg5LgeLrVldLg8_xthk[/img] e [br][br][img width=391,height=59]https://lh3.googleusercontent.com/Jl3WpjsF9S6sQDbHpqTWS8Ua_McbXRSUk9UoFpBxiYHcjIZZwnxy1EYbN_5smwyVkpC92DO3_eOHaoGrk3x42xJ6FrBd614CrL0r5kzLfzq_xzwmOAKzQut6w46RMxwD7rlfviCO1cTwHVty4AusSUE[/img] [img width=85,height=36]https://lh4.googleusercontent.com/tXJvs1KZlkOnkEjE6b7BUPP6_wRIZNciest4xcvsnIgzpf4hRIgGzZXc_9na4TOTnQ7VzKVCvn64F3HnOvg9qOL4WKVnQML4cki9zoRKcPCJmVr3QNjhJ6F_E2slHuIy8eg-O4HF6DWtH2YIV_dIzrE[/img].[br][br]A superfície pode ser representada na forma vetorial[br][br] [img width=265,height=20]https://lh4.googleusercontent.com/lxvb109nA9WRLPJK-kql8mVHOBntuCHiNL1Ns2VX9u6mm5Zws17Zxbh1_O1wnVsOWM9Mpt3fSaWb-sie1P_k9X98V-bnScoUyVLNbT8iTDe1qkbhFfBlybf0USMllN67JB2Q9dKEDJb1qAcXOcDHs60[/img] [br][br] [img width=328,height=40]https://lh4.googleusercontent.com/Cs8VLRGrii2SRNYZdmozYSk3MWXsvqmIzIGMf3xLwaFItVlI3AHfDtKn7He9tnd3-GEPuLmDh9D5WX71LaY_Jvm-qKBhdNh0gD0xOpScU1kdnB-VDsaVcM9I3r2LHRYsvStVNj8pEW87niNAuJvgBEI[/img].[br][br]com [img width=100,height=17]https://lh4.googleusercontent.com/YbuX8wIpfjdwRG8JWoVeL6aVUMoQPP0KwJHmCSBJ5EQbyNXYI32RwlVcVH57Y8HlgNPaQm1_1kp_OOtfMCgDUdH2yjYVfXpK1XUC4FHsSOfKjTXRnYgmj09cQ3s44fq1QXscDFwk64m81gr91FuBGdE[/img] e [img width=91,height=16]https://lh4.googleusercontent.com/03drm3WlJEb0YGcHqUrNSEOHG8-4Fp7IfKDvB_MgjvLonylfN1ID1P80TlgJTznbhE1nHS2xxYCOht7XuqpkQQylM44zZQ2sR-rzGSo1LpUvP9htRQWNXij-laFUoAJh9ZGzDjMZ1v4mdWkzKwWJ9cc[/img].[br][br]Assim,[br][br][img width=396,height=36]https://lh6.googleusercontent.com/AtmL5BummBYsLM-TwawEZ0uWITAxi2kI0I_hpTQv8t8yF9nqH3b5qcuLv0s6hbE6DelBImjBwhIIvDCFVDx3Hh_gDb5-g0H8rn--sx9JeDNcFGk6DZBI1WIM7k-1XNyV6fdGaZsm4O7nYi1WPG-Fk2o[/img][br][br][img width=224,height=36]https://lh4.googleusercontent.com/fqdWGwi7hS-NxGSMWmJLXsby9QtCxf_TzxarywNOHnpXHbAkooFmF4EWmocqIgXVbcDq6ctzeflZ9yP692z8hSPBivL46PHXyrmxlCbtVQ6RNUSBjTp6ZHGmhgfLmYerQi4HV8-hyeTLoxezxoJ2Dzc[/img][br][br]Logo, temos o produto vetorial definido por[br][br][br][img width=64,height=36]https://lh5.googleusercontent.com/g6Jrh5F0jNcIVZbWXT_bVZFpTxI_LPsBb4UahJpqg6s8MYurQdzsfjLXlssoIjAYOVdAh6kXn8M387BVtHbeSsX75iazuclCgHNTJxqY5EzunyIxD9SSyc5PTp3v24GkAKGkvc8lOy_oMX_wCaoSO7o[/img] [img width=344,height=80]https://lh5.googleusercontent.com/rPLzITv5jXoSsTosBkoYLO2AOd0K1g1KfjWhkNv6TPgL1WBSPbkLHlllCIEMT_-bFqtPHw4Ldku2hKwCFmBXjyBkmv8jOtJKvxZuL-1fio4BX6lNbQ9L4OhLP_Gyl0iTgLVuXwFTf2EUc-hVG9DJ-hg[/img][br][br][img width=831,height=37]https://lh5.googleusercontent.com/nq8iOQ2j7kymPa2gCq48fbB4GmXbo6t-RdRPeCf5xl6kj8NfAGBUVn_swOVHXWmFBLQI9LjmsUJDuZvHeueeQuG-BJIhIhd3NHHkIvOC5k-1ITiKu8i2u9Nqfm-kepx8gjp0teyyGyPaa_CmdDTJHtA[/img].[br][br][br]Para calcular a área da superfície, basta calcular a integral definida abaixo com o integrando sendo o módulo do produto vetorial das derivadas parciais.[br][br][img width=189,height=41]https://lh4.googleusercontent.com/BQ0rghUVI_35Kezozs3IK4XKQR2oMrmDO5MYnnSGnjgwigir90ghr3TISzESu0z7wZK0nixWFWuW1lEUJ0GBBVpz1plQ1nV6hK8-7m34sgxx8H76xdmEOe4AjtFkudDotQxfBJZTgr1VzEhW0Vm-API[/img][br][br][img width=1020,height=52]https://lh5.googleusercontent.com/R8GrmoR-Nra6vc-7oI-KV7oC03CM47fC8XR4DPgsV764IF9-8nxEY7hgCyXFkbVbbwjYY116qZ-z3LDKEcggAX_K-FjNwg8e3DqOUhn7CvDeU7nGCY4faYjxE7fLIUZZB_zcHVVze9JgB7siEt8ambw[/img][br][br].[br][br][br][br][br][br][br][br][br][br][br][br][br][br]