Constant speed

04112016, 02:01 PM
Post: #9




RE: Constant speed
The function \(y=sin(x)\) has the slope \({dy\over dx}=cos(x)\) which yields
\[dy=cos(x) \cdot dx\] The arc length of a segment with components \(dx\) by \(dy\) is given by \[ds = \sqrt{dx^2+dy^2}\] Substituting \(dy\) into the above yields \[ds = \sqrt{dx^2+(cos(x) \cdot dx)^2}\] and solving for \(dx\) gives \[dx = {ds \over \sqrt{cos(x)^2 + 1}}\] For any station \(x\) this defines the required \(dx\) to obtain the desired \(ds\). Useful for plotting curves using constant segment lengths or constant speed driving on a curved road ;) The "General" answer depends on the equation  not all have simple Solutions for \(dx\). Then some nonlinear solver resp. iteration would be needed. 

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Messages In This Thread 
Constant speed  Tugdual  04042016, 10:33 PM
RE: Constant speed  PANAMATIK  04052016, 07:01 AM
RE: Constant speed  Tugdual  04052016, 07:19 AM
RE: Constant speed  Dave Britten  04052016, 11:14 AM
RE: Constant speed  Tugdual  04052016, 06:04 PM
RE: Constant speed  Dave Britten  04062016, 11:16 AM
RE: Constant speed  Tugdual  04072016, 06:13 AM
RE: Constant speed  Dave Britten  04072016, 11:16 AM
RE: Constant speed  Martin Hepperle  04112016 02:01 PM
RE: Constant speed  Tugdual  04112016, 03:53 PM
RE: Constant speed  Martin Hepperle  04132016, 03:29 PM
RE: Constant speed  Tugdual  04132016, 06:30 PM
RE: Constant speed  Martin Hepperle  04182016, 07:27 AM

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