View Full Version : Time Compression/Dilation
cecil_kirksey@atk.com
Dec1-04, 11:07 AM
<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>Hi:\nI am trying to generate the physically correct expression for the time\ndilated or compressed signal received by a monostatic radar, which has\na high inertial velocity and acceleration, from a stationary point\ntarget. I am familar with the derivations in Kelly\'s IEEE MIL 1965\npaper and Chapter 3 in Skolnik\'s radar handbook. The problem that I\nseem to be having is that Kelly\'s paper does not differentiate between\nan accelerating target or radar. But the scenario is asymmetrical.\nReferences on relativity with accelerated observers seem to clearly\nindicate a difference between the two scenarios. I am trying to\nsimulate the processed IF signal for the radar and therefore need a\nvalidated, i.e., physically correct, signal model. Typical numbers for\nthis problem are 1000m/s, 100g\'s, 20ms CPI and 94GHz f0. If anyone\nwould care to engage in a correspondence regarding this problem I would\ngreatly appreciate it.\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>Hi:
I am trying to generate the physically correct expression for the time
dilated or compressed signal received by a monostatic radar, which has
a high inertial velocity and acceleration, from a stationary point
target. I am familar with the derivations in Kelly's IEEE MIL 1965
paper and Chapter 3 in Skolnik's radar handbook. The problem that I
seem to be having is that Kelly's paper does not differentiate between
an accelerating target or radar. But the scenario is asymmetrical.
References on relativity with accelerated observers seem to clearly
indicate a difference between the two scenarios. I am trying to
simulate the processed IF signal for the radar and therefore need a
validated, i.e., physically correct, signal model. Typical numbers for
this problem are 1000m/s, 100g's, 20ms CPI and 94GHz f0. If anyone
would care to engage in a correspondence regarding this problem I would
greatly appreciate it.
<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>\nAs nobody replied, here\'s my two cents.\n\n<cecil_kirksey@atk.com> wrote in message\nnews:1101904373.016864.175800@z14g2000cwz .googlegroups.com...\n> Hi:\n> I am trying to generate the physically correct expression for the time\n> dilated or compressed signal received by a monostatic radar, which has\n> a high inertial velocity and acceleration, from a stationary point\n> target.\n\nWhat is "inertial velocity"?\n\n> I am familar with the derivations in Kelly\'s IEEE MIL 1965\n> paper and Chapter 3 in Skolnik\'s radar handbook. The problem that I\n> seem to be having is that Kelly\'s paper does not differentiate between\n> an accelerating target or radar. But the scenario is asymmetrical.\n\nThat\'s surprising. Regretfuly I don\'t know those books, so I can\'t help you\nthere.\n\n> References on relativity with accelerated observers seem to clearly\n> indicate a difference between the two scenarios. I am trying to\n> simulate the processed IF signal for the radar and therefore need a\n> validated, i.e., physically correct, signal model. Typical numbers for\n> this problem are 1000m/s, 100g\'s, 20ms CPI and 94GHz f0. If anyone\n> would care to engage in a correspondence regarding this problem I would\n> greatly appreciate it.\n\nIf you post this in sci.physics.relativity you may get satisfactory replies,\nsome people are really helpful for this kind of questions. I can help you\nwith one additional certainty: indeed the Lorentz transforms are only valid\nfor inertial reference frames.\nBut from calculations with the Lorentz transforms you may establish what the\nmoving radar will detect: just base all calculations on the "stationary"\nframe and keep track of the position of the radar. As long as the radar\nrefers to the stationary frame there is no problem, just as for GPS.\nAlternatively you could use ready-made SRT equations for accelerating frames\nthat were derived from the Lorentz transforms. If I remember well that was\nfirst done by Builder, I should have the paper (PDF) somewhere.\n\nSuccess!\nHarald\n\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>As nobody replied, here's my two cents.
<cecil_kirksey@atk.com> wrote in message
news:1101904373.016864.175800@z14g2000cwz.googlegr oups.com...
> Hi:
> I am trying to generate the physically correct expression for the time
> dilated or compressed signal received by a monostatic radar, which has
> a high inertial velocity and acceleration, from a stationary point
> target.
What is "inertial velocity"?
> I am familar with the derivations in Kelly's IEEE MIL 1965
> paper and Chapter 3 in Skolnik's radar handbook. The problem that I
> seem to be having is that Kelly's paper does not differentiate between
> an accelerating target or radar. But the scenario is asymmetrical.
That's surprising. Regretfuly I don't know those books, so I can't help you
there.
> References on relativity with accelerated observers seem to clearly
> indicate a difference between the two scenarios. I am trying to
> simulate the processed IF signal for the radar and therefore need a
> validated, i.e., physically correct, signal model. Typical numbers for
> this problem are 1000m/s, 100g's, 20ms CPI and 94GHz f0. If anyone
> would care to engage in a correspondence regarding this problem I would
> greatly appreciate it.
If you post this in sci.physics.relativity you may get satisfactory replies,
some people are really helpful for this kind of questions. I can help you
with one additional certainty: indeed the Lorentz transforms are only valid
for inertial reference frames.
But from calculations with the Lorentz transforms you may establish what the
moving radar will detect: just base all calculations on the "stationary"
frame and keep track of the position of the radar. As long as the radar
refers to the stationary frame there is no problem, just as for GPS.
Alternatively you could use ready-made SRT equations for accelerating frames
that were derived from the Lorentz transforms. If I remember well that was
first done by Builder, I should have the paper (PDF) somewhere.
Success!
Harald
cecil_kirksey@atk.com
Dec11-04, 03:07 AM
<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>Thanks for the response Harald. Some clarification of the problem. The\ndilation/compression factor, alpha, for a constant speed between source\nand target is given by alpha = (1-beta)/(1+beta) where beta = V/c. In\nKelly\'s paper he derives an expression by basically using a Taylor\nseries for the round trip delay between the radar (source) and the\ntarget. His expression is basically alpha\' = alpha - A*t/c/(1+beta)^3.\nWhere A is the uniform acceleration as measured in the radar frame and\nt is the duration of the radar signal or period of acceleration. If I\nassume a period of acceleration of T then I would expect that the\nalpha\' should be equal to\n(1-(beta+A*T/c))/(1+(beta+A*T/c)). However, these two expressions are\nnot equal. Kelly\'s derivation makes sense to me but the check for the\nalpha factor at the end of the acceleration does not. I have tried to\nexpand the alpha expression using a Taylor series and do not get\nKelly\'s result. (Not that I would necessarily expect to but that would\nhave been nice.) I also tried integrating the derivative of alpha over\nthe T second interval. Since the alpha value is theoritically correct\nand exact I would have thought that using a Taylor series expansion to\naccount for the acceleration would work. This seems like a simple\nenough problem that should have a ready made answer. I guess I will\nhave to get serious and try the accelerated frame derivation using\nstandard STR.\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>Thanks for the response Harald. Some clarification of the problem. The
dilation/compression factor, \alpha, for a constant speed between source
and target is given by \alpha = (1-\beta)/(1+\beta) where \beta = V/c. In
Kelly's paper he derives an expression by basically using a Taylor
series for the round trip delay between the radar (source) and the
target. His expression is basically \alpha' = \alpha - A*t/c/(1+\beta)^3.
Where A is the uniform acceleration as measured in the radar frame and
t is the duration of the radar signal or period of acceleration. If I
assume a period of acceleration of T then I would expect that the
\alpha' should be equal to
(1-(\beta+A*T/c))/(1+(\beta+A*T/c)). However, these two expressions are
not equal. Kelly's derivation makes sense to me but the check for the
\alpha factor at the end of the acceleration does not. I have tried to
expand the \alpha expression using a Taylor series and do not get
Kelly's result. (Not that I would necessarily expect to but that would
have been nice.) I also tried integrating the derivative of \alpha over
the T second interval. Since the \alpha value is theoritically correct
and exact I would have thought that using a Taylor series expansion to
account for the acceleration would work. This seems like a simple
enough problem that should have a ready made answer. I guess I will
have to get serious and try the accelerated frame derivation using
standard STR.
cecil_kirksey@atk.com
Dec13-04, 11:08 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>the creation of this\ncommunity was an improvement, but at any rate it satisfied the\npioneer\'s need for the power process.\n\n58. It would be possible to give other examples of societies in which\nthere has been rapid change and/or lack of close community ties\nwithout he kind of massive behavioral aberration that is seen in\ntoday\'s industrial society. We contend that the most important cause\nof social and psychological problems in modern society is the fact\nthat people have insufficient opportunity to go through the power\nprocess in a normal way. We don\'t mean to say that modern society is\nthe only one in which the power process has been disrupted. Probably\nmost if not all civilized societies have interfered with the power \'\nprocess to a greater or lesser extent. But in modern industrial\nsociety the problem has become particularly acute. Leftism, at least\nin its recent (mid-to-late -20th century) form, is in part a symptom\nof deprivation with respect to the power process.\n\nDISRUPTION OF THE POWER PROCESS IN MODERN SOCIETY\n\n\n\n59. We divide human drives into three groups: (1) those drives that\ncan be satisfied with minimal effort; (2) those that can be satisfied\nbut only at the cost of serious effort; (3) those that cannot be\nadequately satisfied no matter how much effort one makes. The power\nprocess is the process of satisfying the drives of the second group.\nThe more drives there are in the third group, the more there is\nfrustration, anger, eventually defeatism, depression, etc.\n\n60. In modern industrial society natural human drives tend to be\npushed into the first and third groups, and the second group tends to\nconsist increasingly of artificially created drives.\n\n61. In primitive societies, physical necessi\n\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>the creation of this
community was an improvement, but at any rate it satisfied the
pioneer's need for the power process.
58. It would be possible to give other examples of societies in which
there has been rapid change and/or lack of close community ties
without he kind of massive behavioral aberration that is seen in
today's industrial society. We contend that the most important cause
of social and psychological problems in modern society is the fact
that people have insufficient opportunity to go through the power
process in a normal way. We don't mean to say that modern society is
the only one in which the power process has been disrupted. Probably
most if not all civilized societies have interfered with the power '
process to a greater or lesser extent. But in modern industrial
society the problem has become particularly acute. Leftism, at least
in its recent (mid-to-late -20th century) form, is in part a symptom
of deprivation with respect to the power process.
DISRUPTION OF THE POWER PROCESS IN MODERN SOCIETY
59. We divide human drives into three groups: (1) those drives that
can be satisfied with minimal effort; (2) those that can be satisfied
but only at the cost of serious effort; (3) those that cannot be
adequately satisfied no matter how much effort one makes. The power
process is the process of satisfying the drives of the second group.
The more drives there are in the third group, the more there is
frustration, anger, eventually defeatism, depression, etc.
60. In modern industrial society natural human drives tend to be
pushed into the first and third groups, and the second group tends to
consist increasingly of artificially created drives.
61. In primitive societies, physical necessi
<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>phenomenon in armies, corporations, political parties, humanitarian\norganizations, religious or ideological movements. In particular,\nleftist movements tend to attract people who are seeking to satisfy\ntheir need for power. But for most people identification with a large\norganization or a mass movement does not fully satisfy the need for\npower.\n\n84. Another way in which people satisfy their need for the power\nprocess is through surrogate activities. As we explained in paragraphs\n38-40, a surrogate activity that is directed toward an artificial goal\nthat the individual pursues for the sake of the "fulfillment" that he\ngets from pursuing the goal, not because he needs to attain the goal\nitself. For instance, there is no practical motive for building\nenormous muscles, hitting a little ball into a hole or acquiring a\ncomplete series of postage stamps. Yet many people in our society\ndevote themselves with passion to bodybuilding, golf or stamp\ncollecting. Some people are more "other-directed" than others, and\ntherefore will more readily attack importance to a s\n\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>phenomenon in armies, corporations, political parties, humanitarian
organizations, religious or ideological movements. In particular,
leftist movements tend to attract people who are seeking to satisfy
their need for power. But for most people identification with a large
organization or a mass movement does not fully satisfy the need for
power.
84. Another way in which people satisfy their need for the power
process is through surrogate activities. As we explained in paragraphs
38-40, a surrogate activity that is directed toward an artificial goal
that the individual pursues for the sake of the "fulfillment" that he
gets from pursuing the goal, not because he needs to attain the goal
itself. For instance, there is no practical motive for building
enormous muscles, hitting a little ball into a hole or acquiring a
complete series of postage stamps. Yet many people in our society
devote themselves with passion to bodybuilding, golf or stamp
collecting. Some people are more "other-directed" than others, and
therefore will more readily attack importance to a s
cecil_kirksey@atk.com
Dec14-04, 10:18 AM
<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>\nThanks for the response Harald. Some clarification of the problem. The\ndilation/compression factor, alpha, for a constant speed between source\nand target is given by alpha = (1-beta)/(1+beta) where beta = V/c. In\nKelly\'s paper he derives an expression by basically using a Taylor\nseries for the round trip delay between the radar (source) and the\ntarget. His expression is basically alpha\' = alpha - A*t/c/(1+beta)^3.\nWhere A is the uniform acceleration as measured in the radar frame and\nt is the duration of the radar signal or period of acceleration. If I\nassume a period of acceleration of T then I would expect that the\nalpha\' should be equal to\n(1-(beta+A*T/c))/(1+(beta+A*T/c)). However, these two expressions are\nnot equal. Kelly\'s derivation makes sense to me but the check for the\nalpha factor at the end of the acceleration does not. I have tried to\nexpand the alpha expression using a Taylor series and do not get\nKelly\'s result. (Not that I would necessarily expect to but that would\nhave been nice.) I also tried integrating the derivative of alpha over\nthe T second interval. Since the alpha value is theoritically correct\nand exact I would have thought that using a Taylor series expansion to\naccount for the acceleration would work. This seems like a simple\nenough problem that should have a ready made answer. I guess I will\nhave to get serious and try the accelerated frame derivation using\nstandard STR.\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>Thanks for the response Harald. Some clarification of the problem. The
dilation/compression factor, \alpha, for a constant speed between source
and target is given by \alpha = (1-\beta)/(1+\beta) where \beta = V/c. In
Kelly's paper he derives an expression by basically using a Taylor
series for the round trip delay between the radar (source) and the
target. His expression is basically \alpha' = \alpha - A*t/c/(1+\beta)^3.
Where A is the uniform acceleration as measured in the radar frame and
t is the duration of the radar signal or period of acceleration. If I
assume a period of acceleration of T then I would expect that the
\alpha' should be equal to
(1-(\beta+A*T/c))/(1+(\beta+A*T/c)). However, these two expressions are
not equal. Kelly's derivation makes sense to me but the check for the
\alpha factor at the end of the acceleration does not. I have tried to
expand the \alpha expression using a Taylor series and do not get
Kelly's result. (Not that I would necessarily expect to but that would
have been nice.) I also tried integrating the derivative of \alpha over
the T second interval. Since the \alpha value is theoritically correct
and exact I would have thought that using a Taylor series expansion to
account for the acceleration would work. This seems like a simple
enough problem that should have a ready made answer. I guess I will
have to get serious and try the accelerated frame derivation using
standard STR.
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