Re: need help determined time to travel a path
- To: mathgroup at smc.vnet.net
- Subject: [mg107552] Re: need help determined time to travel a path
- From: Narasimham <mathma18 at gmail.com>
- Date: Tue, 16 Feb 2010 06:11:31 -0500 (EST)
- References: <hlb8oj$rk0$1@smc.vnet.net> <hldm94$15i$1@smc.vnet.net>
continued.. (* You are attempting to use advanced CAS Mathematica perhaps without adequate prior paper and pencil work. Letting {x,y}=R {Cos[th],Sin[th]} ; dt =ds /Sqrt[2 g y] ; dt/dth= - Sqrt[R/2g]/Sqrt[Sin[th]] ; the time integrates to Sqrt[2R/g]*EllipticF[th/2,2] in terms of Elliptic Integral ; A particle takes ~ 2.6 seconds from top to bottom in a circle of diameter 9.8 meters *) t= Integrate[-1/Sqrt[Sin[th]],th] 2 EllipticF[1/2 (Pi/2-th),2] Plot[% ,{th,0,Pi}] HTH Narasimham