New tie paradigm - Revision history

PhiNotPi: Fixed typos

2014-02-15T00:19:14Z

Fixed typos

Numsgil at 07:02, 26 November 2006

2006-11-26T07:02:47Z

Numsgil at 06:57, 26 November 2006

2006-11-26T06:57:41Z

Numsgil: /* Rotational Drag */

2006-06-25T04:37:06Z

‎Rotational Drag

Numsgil: /* Tie Notes */

2006-06-25T03:36:08Z

‎Tie Notes

Numsgil: /* Sysvars */

2006-06-25T03:34:38Z

‎Sysvars

Numsgil: /* Basics */

2006-06-25T03:33:27Z

‎Basics

Sprotiel: /* Drag forces */ added expressions for the force when alpha=2

2006-05-08T16:49:24Z

‎Drag forces: added expressions for the force when alpha=2

Sprotiel: /* Tie physics (redone) */calculations done!

2006-05-08T16:32:16Z

‎Tie physics (redone): calculations done!

Numsgil: /* Translational Drag */

2006-05-05T01:36:49Z

‎Translational Drag

@@ Line 6: / Line 6: @@
 ''Hard'' ties are totally rigid bodies, with a set length.  Bots can "flash" the tie for a cycle, allowing it to change length.  Bots apply a force along the length of the tie.  After this, the tie ceases to exist for a cycle, allowing the bots on either end to move to a new position.  The tie then reappears, and carries on as normal.
-Ties connect to bots using a [http://science.howstuffworks.com/bearing1.htm radial bearing], so that the rotation of the tie and the rotation of the bot are independant of each other.  Bots can "freeze" the the bearings of hard ties, basically locking the tie and the bot together.  This can be done to "freeze" the relative angles of a tie with respect to the bot.
+Ties connect to bots using a [http://science.howstuffworks.com/bearing1.htm radial bearing], so that the rotation of the tie and the rotation of the bot are independent of each other.  Bots can "freeze" the the bearings of hard ties, basically locking the tie and the bot together.  This can be done to "freeze" the relative angles of a tie with respect to the bot.
 Bots can apply forces to two hard ties to change the angle between them, rather similar to how muscles are used to move bones in the human body (the specifics of this are still in progress).
@@ Line 18: / Line 18: @@
 :When settie isn't set, writetie removes an extra value from the stack to represent the tie being pointed to.  ie: -1 10 .up writetie to write to tie -1.
-:If a negative memory location is specified (ie: 10 -1 writetie) substance transfer is initiated.  10 -1 writetie would transfer 10 units of energy from the tie being pointed to.  If settie is unset, this vesion also takes an additional value form the stack.
+:If a negative memory location is specified (ie: 10 -1 writetie) substance transfer is initiated.  10 -1 writetie would transfer 10 units of energy from the tie being pointed to.  If settie is unset, this version also takes an additional value form the stack.
-*settie - Sets the current tie that the DNA is looking at.  When a new tie is set, all the sysvars update for the new information from that tie.  Negative nubmers specify a physical tie in the internal array.  Positive numbers specifies a tie phase.  Multiple ties can be addressed through a single tie phase.
+*settie - Sets the current tie that the DNA is looking at.  When a new tie is set, all the sysvars update for the new information from that tie.  Negative numbers specify a physical tie in the internal array.  Positive numbers specifies a tie phase.  Multiple ties can be addressed through a single tie phase.
 *nexttie - settie's to the next tie.  If settie is currently set to negative (ie: internal arrays) it finds the next tie in the internal array.  If the present tie is already at the end, it moves back to the beginning.  If the present tie is positive, nexttie finds the next valid tie phase, looping back to the lowest tie phase if it's already at the highest.  If settie is unset (ie: set to 0) nexttie pushes it to first internal tie (ie: a negative).
@@ Line 33: / Line 33: @@
 *currtie - The value that settie is set to.  A read sysvar.
-*numties - Returns the number of phsyical ties connected to the bot.
+*numties - Returns the number of physical ties connected to the bot.
 *recentport, recentphase - Returns the phase and port of the most recently formed tie ''with a cycle delay''.
@@ Line 41: / Line 41: @@
 == Tie Notes ==
-*Ports - The internal array index is referred to as a tie's "port".  Each tie has a unique port.  Each port may or may not have a tie.  Port ranges are set by the number of ties in existance when a new tie is formed.  Ties always fill in the first gap in the internal tie array.
+*Ports - The internal array index is referred to as a tie's "port".  Each tie has a unique port.  Each port may or may not have a tie.  Port ranges are set by the number of ties in existence when a new tie is formed.  Ties always fill in the first gap in the internal tie array.
 *Phase - The phase of a tie is a way of addressing multiple ties at once.  Each tie has a unique phase.  Phases may exist anywhere in the mod range [1,200].  That is, 1 = 201 = 401.
@@ Line 50: / Line 50: @@
 == Tie Physics ==
-Tie physics has been alot of work, and alot of calculus, but I think the below is accurate.  It still will need to be double checked, as it's been many months since I did the work.
+Tie physics has been a lot of work, and a lot of calculus, but I think the below is accurate.  It still will need to be double checked, as it's been many months since I did the work.
-Fluid forces on ties can be segmented into two seperate parts: those that cause rotation of the tie and those that cause translation of the tie.
+Fluid forces on ties can be segmented into two separate parts: those that cause rotation of the tie and those that cause translation of the tie.
 Ties are defined by two endpoints, the two bots.
@@ Line 155: / Line 155: @@
 The exact way in which the drags are divided up I haven't worked out yet, but I don't imagine it should be too terribly difficult (jinxed myself :P).
-The main theoretical issue I have is with the possibility that I'm doubling up the forces by calculating both the translational and rotational Drag seperately and applying them seperately, but I don't think this is the case, and even if it is it's just increasing by a constant factor, which is a minor issue.
+The main theoretical issue I have is with the possibility that I'm doubling up the forces by calculating both the translational and rotational Drag separately and applying them separately, but I don't think this is the case, and even if it is it's just increasing by a constant factor, which is a minor issue.
 == Tie physics (redone) ==

@@ Line 4: / Line 4: @@
 ''Soft'' ties, such as birth ties and ties under 100 cycles old, act as springy telescoping rods.  They will constantly push to return to their creation length, though this force is damped to achieve stability.
-''Hard'' ties are totally rigid, never changing length (this may change in the future).  They connect to bots using a [http://science.howstuffworks.com/bearing1.htm radial bearing], so that the rotation of the tie and the rotation of the bot are independant of each other.  Bots can "freeze" the the bearing with specific ties, basically locking the tie and the bot together.  This can be done to "freeze" the relative angles of a tie with respect to the bot.
+''Hard'' ties are totally rigid bodies, with a set length.  Bots can "flash" the tie for a cycle, allowing it to change length.  Bots apply a force along the length of the tie.  After this, the tie ceases to exist for a cycle, allowing the bots on either end to move to a new position.  The tie then reappears, and carries on as normal.
-Bots can apply forces to two ties to change the angle between them, rather similar to how muscles are used to move bones in the human body (the specifics of this are still in progress).
+Ties connect to bots using a [http://science.howstuffworks.com/bearing1.htm radial bearing], so that the rotation of the tie and the rotation of the bot are independant of each other.  Bots can "freeze" the the bearings of hard ties, basically locking the tie and the bot together.  This can be done to "freeze" the relative angles of a tie with respect to the bot.
 == Commands ==

@@ Line 2: / Line 2: @@
 == Basics ==
-Ties are considered to be perfectly rigid telescoping rods.  They connect to bots using a [http://science.howstuffworks.com/bearing1.htm radial bearing], so that the rotation of the tie and the rotation of the bot are independant of each other.  Bots can "freeze" the the bearing with specific ties, basically locking the tie and the bot together.  This can be done to "freeze" the relative angles of a tie with respect to the bot.
+''Soft'' ties, such as birth ties and ties under 100 cycles old, act as springy telescoping rods.  They will constantly push to return to their creation length, though this force is damped to achieve stability.
 Bots can apply forces to two ties to change the angle between them, rather similar to how muscles are used to move bones in the human body (the specifics of this are still in progress).

← Older revision		Revision as of 04:37, 25 June 2006
Line 127:		Line 127:

	Rotational Drag is also divided up between bot A and B depending on their masses and distance from xc.		Rotational Drag is also divided up between bot A and B depending on their masses and distance from xc.
		+
		+	Note that if a = b, Rotational Drag is 0 (since the tie isn't rotating).

	=== Rigid Tie velocity normalization ===		=== Rigid Tie velocity normalization ===

@@ Line 41: / Line 41: @@
 *Phase - The phase of a tie is a way of addressing multiple ties at once.  Each tie has a unique phase.  Phases may exist anywhere in the mod range [1,200].  That is, 1 = 201 = 401.
-*Length - Max tie length will be 1000, after which all ties become 100% rigid and acts like a stiff rod.  This includes birth ties.  A later feature will be that the max tie length is a function of the amount of material (nrg) used in its construction.  Ties' diameter will stretch and shrink as the tie does.  Ties won't be allowed to go below a certain diameter.  This diameter will also effect the bandwidth (that is, the max throughput) allowed in sharing/stealing substances.
+*Length - Ties cannot be longer than 1000 twips (a typical bot is 120 twips in diameter).  This includes birth ties.  Later the max tie length will be a function of the amount of material (nrg) used in its construction.  Ties' diameter will stretch and shrink as the tie does.  Ties won't be allowed to go below a certain diameter.  This diameter will also effect the bandwidth (that is, the max throughput) allowed in sharing/stealing substances.
 *Birth Ties - Spring ties that after 100 cycles die off or harden depending on the value set on birthtietype.  Birth ties are only formed between a mother and child bot at the moment of reproduction.

@@ Line 19: / Line 19: @@
 == Sysvars ==
-*readtielen - A read sysvar.  Reads back the length of the current tie.
+*tielen - A read/write sysvar.  reads back the ties natural length.  If this value is overwritten, the ties natural length is set to the new value.
 *tieangle - A read sysvar.  Reads back the relative angle of the tie with respect to the bot's eye.

@@ Line 199: / Line 199: @@
 <math> -T = L^2 f \epsilon_A \frac{3 w_B^3 - w_B^2 w_A - w_B w_A^2 - w_A^3}{12(w_B-w_A)}</math>
-<math> -T = \frac{L^2 f \epsilon_A}{12}(3 w_B^2 + 2 w_B w_A + w_A^2)</math>
+<math> -T = \frac{L^2 f \epsilon_A}{12}(3 w_B^2 + 2 w_B w_A + w_A^2)</math> and <math> F_B = -\frac{L f \epsilon}{12}(3 w_B^2 + 2 w_B w_A + w_A^2)</math>
 If w<sub>A</sub> and w<sub>B</sub> have opposite signs,
-<math> T = L^2 f \epsilon_A \frac{- w_B^3}{3(w_B-w_A)}- L^2 f\epsilon_A \frac{- w_B^4 - w_A^4}{12(w_B-w_A)^2}</math>
+<math> -T = L^2 f \epsilon_A \frac{- w_B^3}{3(w_B-w_A)}- L^2 f\epsilon_A \frac{- w_B^4 - w_A^4}{12(w_B-w_A)^2}</math>
-<math> T = L^2 f \epsilon_B \frac{3 w_B^4 - 4 w_B^3 w_A - w_A^4}{12(w_B-w_A)^2}</math>, with no possible simplification.
+<math> -T = L^2 f \epsilon_B \frac{3 w_B^4 - 4 w_B^3 w_A - w_A^4}{12(w_B-w_A)^2}</math> and <math> F_B = -L f \epsilon_B \frac{3 w_B^4 - 4 w_B^3 w_A - w_A^4}{12(w_B-w_A)^2}</math> , with no possible simplification.

@@ Line 159: / Line 159: @@
 *'''v<sub>A</sub>''' and '''v<sub>B</sub>''' their velocities (<tt>botA.vel</tt> and <tt>botB.vel</tt> in the code)
 *L = ||'''r<sub>B</sub>'''-'''r<sub>A</sub>'''|| the length of the tie and '''u''' the unit vector such that '''r<sub>B</sub>'''-'''r<sub>A</sub>''' = L '''u'''.
-*'''n''' the ?/2-rotation of '''u''', so that ('''u''', '''n''') is a direct orthonormal base.
+*'''n''' the ?/2-rotation of '''u''', so that ('''u''', '''n''') is a direct orthonormal base. We'll denote the components of any vector '''x''' in this base as '''x''' = x<sub>T</sub> '''u''' + x<sub>N</sub>'''n'''
 Let's also label the points of the ties by a parameter x in [0;1]. '''r'''(x) = '''r<sub>A</sub>''' +L x '''u''' and the corresponding velocity is '''v'''(x) = (1-x)'''v<sub>A</sub>''' + x '''v<sub>B</sub>'''.
-Now, the drag force acting on an infinitesimal portion of the tie between the positions '''r'''(x) and '''r'''(x+dx) is '''dF''' = f |'''v'''.'''n'''|<sup>&alpha; - 1</sup> ('''v'''.'''n''') '''n''', with &alpha; = 1 if viscosity is the dominating influence on drag and &alpha; = 2 if it's turbulence. f is a coefficient defining the magnitude of drag, it is assumed independent of the length of the tie.
+Now, the drag force acting on an infinitesimal portion of the tie between the positions '''r'''(x) and '''r'''(x+dx) is '''dF''' = -L dx . f |'''v'''.'''n'''|<sup>&alpha; - 1</sup> ('''v'''.'''n''') '''n''', with &alpha; = 1 if viscosity is the dominating influence on drag and &alpha; = 2 if it's turbulence. f is a coefficient defining the magnitude of drag, it is assumed independent of the length of the tie.

← Older revision		Revision as of 01:36, 5 May 2006
Line 76:		Line 76:

	=== Translational Drag ===		=== Translational Drag ===
		+	Translational drag slows a tie moving through the liquid. For instance, if two bots are moving with identical velocity vectors that are not parallel to the tie between them, translational drag on the tie would serve to slow these two bots down.
		+
	<math>\Large Force_{Drag} = \rho r CD(\bar{v}) \int_0^L{v(x)^2 \hat{v(x)} dx}</math>		<math>\Large Force_{Drag} = \rho r CD(\bar{v}) \int_0^L{v(x)^2 \hat{v(x)} dx}</math>