Doug Goncz
Apr21-04, 03:25 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I\'ve been using Mathcad\'s rkadapt (adaptive step size Runge-Kutta) solver to\ndetermine the position and speed of a bicycle using a force balance to specify\nthe second derivative of position, that is, acceleration. The problem is, it\nuses a terrain lookup table that is distance based and I start by estimating\nthe trip will proceed in first gear the whole way at 2 mph. When I define an\ninterval of integration that large, much time is wasted, and all the results\nwith position value greater than the length of the trip are useless.\n\nI think what I have here is a two point boundary value problem.\nCan you confirm this?\n\nI know the position (0) at the start of the trip. I know its value at the end\n(say 27313 feet). I know the speed at the start of the trip (0). I don\'t know\nits value at the end. It hardly matters.\n\nIn the description of the sbval function, I read these hopeful words:\n\n* You have an nth order differential equation.\n* You know some but not all of the value of solution and its first n-1\nderivatives at the beginning of the interval of integration, x1\n* You know some but not all of the values of the solution and its first n-1\nderivatives at the end of the interval of integration, x2\n* Between what you know about the solution at x1 and what you know about it at\nx2, you have n known values.\n\nIn This case at time t1, s. 1 = 0, and s\'.2 = 0. At time t2, s.2 = Distance\ntraveled. t1 = 0. t2 is unknown. What I really want is t2, not the value of s\'2\nat t2. I don\'t care about the finish line conditions. It isn\'t a race, it\'s a\nshopping trip.\n\nBut the sbval function _still_ requires me to input t1 and t2 as x1 and x2\nabove, so it\'s just not right.\n\nNow if I wrote the equation as a differential in _distance_ I\'d be all set. I\'d\njust input x1 = start and x2 = finish, and know t1 = 0 and s\'1=0. But s\'1 has\nto be a derivative of distance, not time, so I must use\n\nSpecific speed\n\nthere.\n\nFor the solver to proceed, I need a variable for specific acceleration, a\nrelation between specific acceleration and specific speed, and the force\nbalance.\n\nLet\'s take this one step at a time, shall we?\n\nA speed of 30 miles per hour is a specific speed of 2 minutes per mile.\n\nAn acceleration of 32.2 feet per second per second isn\'t a distance specific\nacceleration. And inverting it won\'t do. That\'d be seconds squared per foot. I\nneed seconds per foot squared. Is there even such a measure? Something tells me\n\n\nd = 1/2 a t^2 ain\'t it.\n\nNow this is interesting. I\'ve got the force balance. I can integrate it on\ndistance to get an energy balance. I can divide it by mass to get acceleration,\nand the solver will handle the derivatives speed and position. The energy\nconditions at start can be completely known. The altitude at the finish is\nknown.\n\nv = d/t by definition\n\nv.i = dd / dt so is\n\na.i = d^2d / dt^2?\n\nspecific speed = dt / dd\n\nspecific acceleration = d / dd ( dt / dd )\n\nI used an energy function in my simulation of a motor/generator --\nultracapacitors augmented bicycle. This made the problem a system of coupled\ndifferential equations.\n\nI _could_ write the _canonical_ system of coupled differential equations\ngoverning motion of a body. The variables are\n\nL, L/T, L/T^2, L/T^3,\nML, ML/T, ML/T^2, ML/T^3\nML^2, ML^2/T, ML^2/T^2, ML^2/T^3\n\nOf these, I know L = s = distance, L/T = speed, L/T^2 = acceleration, L/T^3 =\njerk, ML = moment (in mechanical engineering), ML/T = impulse, ML/T^2 = force,\nML/T^3 = masscontrol, ML^2 = action, ML^2/T = ?, ML^2/T^2 = energy, and\nML^2/T^3 = power.\n\nAt the start of the problem distance = 0, power input = 80 watts constant\nthroughout, energy = the potential energy at the starting altitude,\nacceleration can be calculated, but the solver finds it, jerk is Dirac, moment\nI\'m not sure about, impulse seems irrelevant, force I have nicely balanced, and\nmasscontrol is also Dirac, action seems like it\'s only used in particle\nphysics, and ML^2/T seems irrelevant but probably is key (energy times time)\n\nThis requires a starting y vector for the rkadapt solver of 12 values. With\nsbval, given s.1 = 0 and s.2 = distance, and a second order equation, the other\n10 can be filled in. Wouldn\'t that be a pretty piece of work?\n\nBut for a coupled system, you need n known value in each of the subsystems, so\nI need now 6 known values. s.1, s.2, v.1, e.1, f.1, and a.1 can all be found,\nso I guess I have 6 and can proceed.\n\nAm I on the right track now, or is it time for one of you dear readers to\nintervene and save me a lot of work?\n\nAm now working with an endocrinologist to control my blood sugar and hormone\nlevels to maximum stability and normality, and should enter NIMH for six months\nsoon so Dr. Michael Egan can image my brain while I withdraw from these\nstinking pharmeceutica oscura, which cross the blood brain barrier and produce\nunmeasureable "results" that deeply disturb the body. He\'ll get a paper out of\nit. The participation is around 300 patients, all starting with psychiatric\nmedication, withdrawing, and restabilizing in a grueling test of ultimate will\nand persistence. I expect his dropout rate is pretty high. What doesn\'t kill us\nmakes us stronger.\n\nDuring withdrawal, Stanford may interview me to see if my symptoms are severe\nenough for their study, which is double blind mifepristone for schizoaffective\ndisorder. Another hormone, this time a stress hormone.\n\nDiet and excercise really help.\n\nThe latest test bicyle is recumbent with a gear range of 657%. What a blast!\nI\'m going to fill the tires with antifreeze solution or water or maybe cherry\nJello to get the flywheel effect disdained by racers. It\'s a Lightning Cycle\nDynamics Thunderbolt. They race the bikes they build. Tim there can output 260\nwatts for an hour! I can do rather less.\n\nMy blood pressure and fats are back to normal.\n\nThings are looking good. Your participation will be greatly appreciated.\n\n\nYours,\n\nDoug Goncz ( ftp://users.aol.com/DGoncz/ )\n\nMy physics project at NVCC:\nhttp://groups.google.com/groups?q=dgoncz&scoring=d plus\n"bicycle", "fluorescent", "inverter", "flywheel", "ultracapacitor", etc.\nin the search box\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I've been using Mathcad's rkadapt (adaptive step size Runge-Kutta) solver to
determine the position and speed of a bicycle using a force balance to specify
the second derivative of position, that is, acceleration. The problem is, it
uses a terrain lookup table that is distance based and I start by estimating
the trip will proceed in first gear the whole way at 2 mph. When I define an
interval of integration that large, much time is wasted, and all the results
with position value greater than the length of the trip are useless.
I think what I have here is a two point boundary value problem.
Can you confirm this?
I know the position (0) at the start of the trip. I know its value at the end
(say 27313 feet). I know the speed at the start of the trip (0). I don't know
its value at the end. It hardly matters.
In the description of the sbval function, I read these hopeful words:
* You have an nth order differential equation.
* You know some but not all of the value of solution and its first n-1
derivatives at the beginning of the interval of integration, x1
* You know some but not all of the values of the solution and its first n-1
derivatives at the end of the interval of integration, x2
* Between what you know about the solution at x1 and what you know about it at
x2, you have n known values.
In This case at time t1, s. 1 = 0, and s'.2 = . At time t2, s.2 = Distance
traveled. t1 = . t2 is unknown. What I really want is t2, not the value of s'2
at t2. I don't care about the finish line conditions. It isn't a race, it's a
shopping trip.
But the sbval function _still_ requires me to input t1 and t2 as x1 and x2
above, so it's just not right.
Now if I wrote the equation as a differential in _distance_ I'd be all set. I'd
just input x1 = start and x2 = finish, and know t1 = and s'1=0. But s'1 has
to be a derivative of distance, not time, so I must use
Specific speed
there.
For the solver to proceed, I need a variable for specific acceleration, a
relation between specific acceleration and specific speed, and the force
balance.
Let's take this one step at a time, shall we?
A speed of 30 miles per hour is a specific speed of 2 minutes per mile.
An acceleration of 32.2 feet per second per second isn't a distance specific
acceleration. And inverting it won't do. That'd be seconds squared per foot. I
need seconds per foot squared. Is there even such a measure? Something tells me
d = 1/2 a t^2[/itex] ain't it.
Now this is interesting. I've got the force balance. I can integrate it on
distance to get an energy balance. I can divide it by mass to get acceleration,
and the solver will handle the derivatives speed and position. The energy
conditions at start can be completely known. The altitude at the finish is
known.
v = d/t by definition
v.i = dd / dt so is
a.i = d^{2d} / dt^2?
specific speed = dt / dd
specific acceleration = d / dd ( dt / dd )
I used an energy function in my simulation of a motor/generator --
ultracapacitors augmented bicycle. This made the problem a system of coupled
differential equations.
I _could_ write the _canonical_ system of coupled differential equations
governing motion of a body. The variables are
L, L/T, L/T^2, L/T^3,
ML, [itex]ML/T, ML/T^2, ML/T^3ML^2, ML^2/T, ML^2/T^2, ML^2/T^3
Of these, I know L = s = distance, L/T = speed, L/T^2 = acceleration, L/T^3 =
jerk, ML = moment (in mechanical engineering), ML/T = impulse, ML/T^2 = force,
ML/T^3 = masscontrol, ML^2 = action, ML^2/T = ?, ML^2/T^2 = energy, and
ML^2/T^3 = power.
At the start of the problem distance = 0, power input = 80 watts constant
throughout, energy = the potential energy at the starting altitude,
acceleration can be calculated, but the solver finds it, jerk is Dirac, moment
I'm not sure about, impulse seems irrelevant, force I have nicely balanced, and
masscontrol is also Dirac, action seems like it's only used in particle
physics, and ML^2/T seems irrelevant but probably is key (energy times time)
This requires a starting y vector for the rkadapt solver of 12 values. With
sbval, given s.1 = and s.2 = distance, and a second order equation, the other
10 can be filled in. Wouldn't that be a pretty piece of work?
But for a coupled system, you need n known value in each of the subsystems, so
I need now 6 known values. s.1, s.2, v.1, e.1, f.1, and a.1 can all be found,
so I guess I have 6 and can proceed.
Am I on the right track now, or is it time for one of you dear readers to
intervene and save me a lot of work?
Am now working with an endocrinologist to control my blood sugar and hormone
levels to maximum stability and normality, and should enter NIMH for six months
soon so Dr. Michael Egan can image my brain while I withdraw from these
stinking pharmeceutica oscura, which cross the blood brain barrier and produce
unmeasureable "results" that deeply disturb the body. He'll get a paper out of
it. The participation is around 300 patients, all starting with psychiatric
medication, withdrawing, and restabilizing in a grueling test of ultimate will
and persistence. I expect his dropout rate is pretty high. What doesn't kill us
makes us stronger.
During withdrawal, Stanford may interview me to see if my symptoms are severe
enough for their study, which is double blind mifepristone for schizoaffective
disorder. Another hormone, this time a stress hormone.
Diet and excercise really help.
The latest test bicyle is recumbent with a gear range of 657%. What a blast!
I'm going to fill the tires with antifreeze solution or water or maybe cherry
Jello to get the flywheel effect disdained by racers. It's a Lightning Cycle
Dynamics Thunderbolt. They race the bikes they build. Tim there can output 260
watts for an hour! I can do rather less.
My blood pressure and fats are back to normal.
Things are looking good. Your participation will be greatly appreciated.
Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/ )
My physics project at NVCC:
http://groups.google.com/groups?q=dgoncz&scoring=d plus
"bicycle", "fluorescent", "inverter", "flywheel", "ultracapacitor", etc.
in the search box
determine the position and speed of a bicycle using a force balance to specify
the second derivative of position, that is, acceleration. The problem is, it
uses a terrain lookup table that is distance based and I start by estimating
the trip will proceed in first gear the whole way at 2 mph. When I define an
interval of integration that large, much time is wasted, and all the results
with position value greater than the length of the trip are useless.
I think what I have here is a two point boundary value problem.
Can you confirm this?
I know the position (0) at the start of the trip. I know its value at the end
(say 27313 feet). I know the speed at the start of the trip (0). I don't know
its value at the end. It hardly matters.
In the description of the sbval function, I read these hopeful words:
* You have an nth order differential equation.
* You know some but not all of the value of solution and its first n-1
derivatives at the beginning of the interval of integration, x1
* You know some but not all of the values of the solution and its first n-1
derivatives at the end of the interval of integration, x2
* Between what you know about the solution at x1 and what you know about it at
x2, you have n known values.
In This case at time t1, s. 1 = 0, and s'.2 = . At time t2, s.2 = Distance
traveled. t1 = . t2 is unknown. What I really want is t2, not the value of s'2
at t2. I don't care about the finish line conditions. It isn't a race, it's a
shopping trip.
But the sbval function _still_ requires me to input t1 and t2 as x1 and x2
above, so it's just not right.
Now if I wrote the equation as a differential in _distance_ I'd be all set. I'd
just input x1 = start and x2 = finish, and know t1 = and s'1=0. But s'1 has
to be a derivative of distance, not time, so I must use
Specific speed
there.
For the solver to proceed, I need a variable for specific acceleration, a
relation between specific acceleration and specific speed, and the force
balance.
Let's take this one step at a time, shall we?
A speed of 30 miles per hour is a specific speed of 2 minutes per mile.
An acceleration of 32.2 feet per second per second isn't a distance specific
acceleration. And inverting it won't do. That'd be seconds squared per foot. I
need seconds per foot squared. Is there even such a measure? Something tells me
d = 1/2 a t^2[/itex] ain't it.
Now this is interesting. I've got the force balance. I can integrate it on
distance to get an energy balance. I can divide it by mass to get acceleration,
and the solver will handle the derivatives speed and position. The energy
conditions at start can be completely known. The altitude at the finish is
known.
v = d/t by definition
v.i = dd / dt so is
a.i = d^{2d} / dt^2?
specific speed = dt / dd
specific acceleration = d / dd ( dt / dd )
I used an energy function in my simulation of a motor/generator --
ultracapacitors augmented bicycle. This made the problem a system of coupled
differential equations.
I _could_ write the _canonical_ system of coupled differential equations
governing motion of a body. The variables are
L, L/T, L/T^2, L/T^3,
ML, [itex]ML/T, ML/T^2, ML/T^3ML^2, ML^2/T, ML^2/T^2, ML^2/T^3
Of these, I know L = s = distance, L/T = speed, L/T^2 = acceleration, L/T^3 =
jerk, ML = moment (in mechanical engineering), ML/T = impulse, ML/T^2 = force,
ML/T^3 = masscontrol, ML^2 = action, ML^2/T = ?, ML^2/T^2 = energy, and
ML^2/T^3 = power.
At the start of the problem distance = 0, power input = 80 watts constant
throughout, energy = the potential energy at the starting altitude,
acceleration can be calculated, but the solver finds it, jerk is Dirac, moment
I'm not sure about, impulse seems irrelevant, force I have nicely balanced, and
masscontrol is also Dirac, action seems like it's only used in particle
physics, and ML^2/T seems irrelevant but probably is key (energy times time)
This requires a starting y vector for the rkadapt solver of 12 values. With
sbval, given s.1 = and s.2 = distance, and a second order equation, the other
10 can be filled in. Wouldn't that be a pretty piece of work?
But for a coupled system, you need n known value in each of the subsystems, so
I need now 6 known values. s.1, s.2, v.1, e.1, f.1, and a.1 can all be found,
so I guess I have 6 and can proceed.
Am I on the right track now, or is it time for one of you dear readers to
intervene and save me a lot of work?
Am now working with an endocrinologist to control my blood sugar and hormone
levels to maximum stability and normality, and should enter NIMH for six months
soon so Dr. Michael Egan can image my brain while I withdraw from these
stinking pharmeceutica oscura, which cross the blood brain barrier and produce
unmeasureable "results" that deeply disturb the body. He'll get a paper out of
it. The participation is around 300 patients, all starting with psychiatric
medication, withdrawing, and restabilizing in a grueling test of ultimate will
and persistence. I expect his dropout rate is pretty high. What doesn't kill us
makes us stronger.
During withdrawal, Stanford may interview me to see if my symptoms are severe
enough for their study, which is double blind mifepristone for schizoaffective
disorder. Another hormone, this time a stress hormone.
Diet and excercise really help.
The latest test bicyle is recumbent with a gear range of 657%. What a blast!
I'm going to fill the tires with antifreeze solution or water or maybe cherry
Jello to get the flywheel effect disdained by racers. It's a Lightning Cycle
Dynamics Thunderbolt. They race the bikes they build. Tim there can output 260
watts for an hour! I can do rather less.
My blood pressure and fats are back to normal.
Things are looking good. Your participation will be greatly appreciated.
Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/ )
My physics project at NVCC:
http://groups.google.com/groups?q=dgoncz&scoring=d plus
"bicycle", "fluorescent", "inverter", "flywheel", "ultracapacitor", etc.
in the search box