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In classical mechanics, the precession of a top under the influence of gravity is not in general, an integrable problem. There are however three famous cases that are integrable, the Euler, the Lagrange and the [[Kovalevskaya Top|Kovalevskaya top]].<ref name = "Audin">Audin, M. Spinning Tops: A Course on Integrable Systems. New York: Cambridge University Press, 1996.</ref> In addition to the energy, each of these tops involves three additional constants of motion that give rise to the [[Integrable system#Hamiltonian systems and Liouville integrability|integrability]].  
If you like the "Canadian Belt Knife" by cold steel (which is created in Taiwan) I would suggest that you genuinely owe it to oneself to check out the original. Welcome to my site! My name is Lucas Bullington, I produced just about every one of the knives you will see in the pages of this web page. Please take pleasure in the pictures, bookmark this site and check back normally.<br><br><br><br>The class act in rod-guided systems is the EdgePro Apex Sharpening Technique. Ben Dale, the owner of EdgePro, has spared no expense in his pursuit of excellence in hand sharpening. The Apex is rugged and utilizes comparatively huge 1 x six inch aluminum oxide waterstones. The angle guide is constantly adjustable for any angle from 10 degrees to over 25 degrees. My measurements confirmed that the angles had been exactly as marked. The Apex comes with a excellent instruction book.<br><br>Due to the hinge pin, no folding knife is as powerful as a [http://www.lezinter.net/wiki/index.php/Schrade_Assisted_Opening_Otf_Knife_Review fixed blade] knife. I as soon as broke the hinge pin in a Buck Folding Hunter by (stupidly) hammering on the back of the blade with a piece of wood. Folding knives are not my selection for separating the ribs from the breastbone or splitting the pelvic bone. Otherwise, they are fine and I practically normally carry a single in the field. The Buck 110 Folding Hunter blends all of these characteristics into a single amazing knife. With its locking mechanism, stainless steel clip-point blade, and iconic legacy, this knife ensures that durability, efficiency and security will be practically assured when making use of this knife. This knife also comes in at a pretty budget-friendly price despite carrying all of the functions suggested!<br><br>Start off by cleaning any residue that may possibly be on the blade. Take a whetstone that has been soaked in water for about 10 minutes. The face side of the blade should really be about 1/eight inch more than the stone. Make sure you do not cut into the whetstone with the sharp cutting edge of the blade. At a 15-20 degree angle, slide the blade back and forth more than the stone evenly and speedily until the blade is sharpened. Turn the knife over and repeat these measures. You can sharpen most knives employing this strategy. How to Hone Your Knife.<br><br>To commence, ask yourself, "How do I intend to use this knife?" If you happen to be searching for a knife that will carry out one particular precise task well — skinning a deer, for instance, or cutting branches around your hunting stand — then you could want to choose a specialty knife created with a single unique objective in thoughts. On the other hand, if you acquire a specialty knife to use as a multi-objective tool for backcountry camping, it likely will not carry out several of the tasks you may have to have it for. Normally start out the choice procedure by picking out a style that's very best suited for the chores the knife is intended to deal with.<br><br>Ring Lock – Although you may possibly not see as many ring locks, they are still extremely simple to use and sturdy as a locking mechanism. It [http://Trac.geekisp.com/uni/ticket/1807 differs] in that you twist a ring if you want to open the knife. When the ring is [http://Sss.chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=%5B%5Biframe+%2F%2Fwww.youtube.com%2Fembed%2Fu9jw1mf_f1I+height%3D%22360%22+width%3D%22640%22%5D%5DSchrade+was+bought+by+Taylor+back+around+2004+just+after+which+most+of+their+line+started+coming+from+China.+Not+saying+you+can%27t+get+high+quality+knives+from+China+as+Spyderco+presents+some+outstanding+models+frombut+Schrade%2FTaylor+isn%27t+Spyderco.%0D%0A%0D%0ASarge+-+Schrade+tends+to+make+Old+Timer%2C+X-Timer+and+Uncle+Henry+knives+as+effectively.+The+one+you+have+pictured+is+a+%22Woodsman%22%2C+I+believe.+There+are+a+couple+in+that+design+but+it+looks+like+the+Woodsman.+9+five%2F8+inch+all+round+andinch+stainless+blade%3F+If+it+is%2C+you+did+okay.+The+MRSP+is+%2437.95.+They+possibly+get+their+iron+ore+from+us+lol.+I+do+not+know%2C+but+I+do+have+pretty+a+handful+of+Schrade%2C+Old-Timer%2C+Uncle+Henry%2C+imperial+pocket+knives+and+they+all+serve+me+nicely.+I+believe+all+are+pre-70%27s%2C+or+very+early+seventies%2C+if+that+suggests+something%2C+none+are+SS.+I+didn%27t+know+Schrade+owned+all+these+brands+or+that+they+use+Chinese+steel.+I+wonder+when+they+started+applying+the+Chinese+steel%3F%3F+Pearl+Harbor+commemorative+knife+from+Schrade+Packaging+-+One+particular+piece+Schrade+box+Knife+Balance%0D%0A%0D%0AAs+I+do+with+all+of+my+knives%2C+I+became+familiar+with+the+Sharpfinger+and+began+its+testing+in+the+kitchen.+This+is+a+great+location+to+see+not+only+how+the+knife+performs+but+how+it+feels+to+the+user.++When+you+loved+this+information+along+with+you+would+want+to+acquire+more+info+about+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fschrade-knives-review%2F+Schrade+Extreme+Survival+Knife+Schf9+Review%5D+kindly+go+to+our+own+web+page.+By+way+of+years+of+practice%2C+I%27ve+discovered+that+how+a+knife+feels+in+use+is+1+of+its+most+essential+attributes.+Immediately+after+a+couple+of+meals%2C+my+intitial+expectations+have+been+realized+as+the+Sharpfinger+felt+excellent+to+me.+My+subsequent+step+was+to+see+how+it+performed+in+day-to-day+use.+Once+again%2C+%5Bhttp%3A%2F%2Fwww.dict.cc%2F%3Fs%3DI%2Bwasn%2527t+I+wasn%27t%5D+%5Bhttp%3A%2F%2FData.Gov.uk%2Fdata%2Fsearch%3Fq%3Ddisappointed+disappointed%5D.%0D%0A%0D%0AI+only+personal+one+particular+other+knife+with+a+ceramic+blade%2C+a+somewhatsmaller+%282-5%2F8%22+blade%2C+four%22+extended+closed%29+StoneRiver+Gear+Premium+Ceramic+Folder+with+bone+deal+with+scales+that+was+provided+to+meby+Jim+Clary+soon+after+his+Guns+and+ShootingOnline+overview+of+these+knives.+The+%5Bhttps%3A%2F%2FWww.google.com%2Fsearch%3Fhl%3Den%26gl%3Dus%26tbm%3Dnws%26q%3Dblade%2Bpattern%26btnI%3Dlucky+blade+pattern%5D+of+the+Stone+River+knifeis+virtually+identical+to+that+of+the+Schrade.+Even+although+it+is+longer%2C+theflat+carbon+fiber+handle+of+the+Schrade+makes+it+lighter+than+the+Stone+Riverknife.+The+construction+and+operation+of+the+two+knives+is+apparently+identicaland+I+would+be+surprised+if+they+had+been+not+sourced+from+the+very+same+factory.%0D%0A%0D%0AThe+Schrade+SCH401L+is+one+particular+of+Taylor+Brands%27%28%29+most+high-priced+folding+knives.+The+2014+MSRP+is%2469.33.+It+is+a+huge%2C+higher+tech+folder+with+a+ceramic+blade+and+carbon+fiberhandle+scales.+The+blade+length+is+3.two%22+and+folded+the+knife+measures4.six%22+long%2C+but+it+weighs+only+two.1+ounces.+Open%2C+the+knife+measures+7.8%22+lengthy.+As+I+took+the+survival+knife+out+of+it+really+is+sheath%2C+my+initial+impression+was+a+mix+of+surprise+and+disbelief.+I+smiled+and+just+waved+the+knife+around+in+my+hand+for+a+when+attempting+to+figure+out+how+in+the+planet+Schrade+was+able+to+place+with+each+other+such+a+formidable+survival+knife+package+for+such+a+crazy+low+on+line+street+price.+See+the+distinction+in+width+compared+to+the+Bear+Grylls+Ultimate+Survival+knife+%3F+Boker+7%E2%80%9D+Ceramic+Santoku+Kitchen+Knife%0D%0A%0D%0Acomparison+for+the+reason+that+the+9+had+clear+purpose+and+sacrificed+any+aesthetic+appeal+to+get+there+even+though+in+the+similar+line+we+now+have+the+ten+giving+customers+an+awful+lot+of+%22nice%22+with+a+lot+more+than+the+money%27s+worth+in+functional+style+options.+This+knife+is+as+%22tactical%22+as+it+is+%22classic%22+and+combines+the+proper+amount+of+the+two+resulting+in+a+incredibly+attractive%2C+high-worth%2C+multi-use+blade.+Quite+nicely+textured+Micarta+scales.+The+overall+length+on+this+OTF+is+8.875+inches%2C+and+the+blade+is+three.75+inches+in+length.+It+weighs+7.72+ounces%2C+has+great+firing+action%2C+and+is+produced+in+the+USA.+When+you+assume+about+that+this+knife+sells+for+just+over+%2420%2C+the+sheath+is+likewise+rather+fantastic.+Thick+natural+leather+with+rivets+and+a+button+retention+clasp.%0D%0A%0D%0AAlthough+neither+of+the+B-side+tracks+come+up+to+really+the+similar+regular+of+vicious+scuzz-jacking+that+Payphone+Player+reaches%2C+both+delve+further+into+the+seam+of+experimental+floor+shakers+that+Schrade+Knives+first+mined.+33140+is+the+heavier+of+the+pair%2C+rolling+in+on+a+breakbeat+carved+entirely+out+of+sinew+and+induced+neurosis%2C+so+rough+it+would+take+your+fingerprints+off+if+you+rested+your+hand+upon+it.+Early+Death+feels+like+a+reprise+of+sorts+of+Schrade+Knives+but+less+sharp%2C+far+more+worn+and+toxic.+Harsh+but+extremely%2C+extremely+fair.+Modern+day+face-pounders+with+the+heart+of+a+dancer.%0D%0A%0D%0AProbably+the+only+drawback+about+this+hollow+deal+with+survival+knife+is+the+sheath+which+is+a+nylon+sheath+with+a+plastic+insert.+The+knife+is+loose+in+it+which+brought+on+the+blade+to+rattle%2C+and+the+knife+can+move+a+few+inches+in+and+out+although+in+the+sheath+causing+a+prospective+circumstance+where+you+could+reduce+yourself.+On+the+other+hand+the+sheath+does+come+with+an+empty+removable+pouch+enabling+you+add+some+additional+gear+to+your+survival+kit.+In+addition%2C+Schrade%27s+other+organization%2C+the+Schrade+Cutlery+Co.%2C+was+sold+in+1946+to+the+Imperial+Knife+Connected+Organizations+thus+becoming+the+Schrade-Walden+Cutlery+Co.%2C+Inc.+Final%2C+in+2004%2C+this+organization+stopped+generating+knives+and+closed+its+factory+and+the+name+was+sold+to+Taylor+Brands+and+employed+for+advertising+purposes.&create=Create twisted] the knife can be folded into the gap and locked by [http://csw1.Vaniercollege.Qc.ca/users/SwapMe/wiki/index.php?title=Schrade_Viper_Otf_Knife_Review twisting additional]. Then to close the blade just do the opposite by twisting the ring folding the blade down and twisting but again. They were well-liked among makers for their affordable expense in making the ring lock.<br><br>These are the upper echelon of knives for several, and are recognized for getting quite high quality blades. Spyderco has worked for years perfecting the ergonomic design and simplicity of their models, giving a clean, functional feel to numerous of them. These practices have endeared the organization to those who rely on their knives in survival scenarios or emergencies such as members of the military, law enforcement, and even some emergency medical teams. Click Here for Full Pricing, Ratings and Testimonials Fixed 3.six four.9 8.5 2.7 4116 German stainless steel Thermo plastic $ four.7 Kershaw 1605 Clash Folding Knife with SpeedSafe Stainless steel – do not rust. Even so, its composition makes it susceptible to denting and other forms of deformation from pressure when sharpened Should you have just about any inquiries concerning where by along with how to employ [http://www.thebestpocketknifereviews.com/schrade-knives-review/ Schrade Knives], you are able to e mail us on our own web site. .
 
The Euler top describes a free top without any particular symmetry, moving in the absence of any external torque. The Lagrange top is a symmetric top, in which the center of gravity lies on the symmetry axis. The [[Kovalevskaya Top|Kovalevskaya top]]<ref name ="kovalevskaya">S. Kovalevskaya, Acta Math. 12 177–232 (1889)</ref><ref name = "Perelemov">A. M. Perelemov, Teoret. Mat. Fiz.,  Volume 131,  Number 2, Pages 197–205 (2002)</ref> is special symmetric top with a unique ratio of the moments of inertia satisfy the relation
 
<math> I_1=I_2= 2 I_3</math>,
 
and in which the center of gravity is located in the plane perpendicular to the symmetry axis.
 
==Hamiltonian Formulation of Classical tops==
 
A classical top<ref name="Goldstein">Herbert Goldstein
Charles P. Poole , John L. Safko, Classical Mechanics, (3rd Edition), Addison-Wesley (2002)</ref> is defined by three principal axes, defined by the three orthogonal vectors <math> \hat{\mathbf{e}}^1</math>, <math> \hat {\mathbf{e}}^2</math> and  <math> \hat{\mathbf{e}}^3</math> with corresponding moments of inertia <math>I_1</math>, <math> I_2</math> and <math>I_3</math>.   In a Hamiltonian formulation of classical tops, the conjugate dynamical variables are the components of the angular momentum vector <math>\vec{L}</math> along the principal axes
 
<math>(l_1, l_2, l_3)= (\vec{L}\cdot \hat {\mathbf{e}}^1,\vec{L}\cdot \hat {\mathbf{e}}^2,\vec{L}\cdot \hat {\mathbf{e}}^3) </math>
 
and the z-components of the three principal axes,
 
<math>(n_1, n_2, n_3)= (\mathbf{\hat{z}}\cdot \hat {\mathbf{e}}^1,\mathbf{\hat{z}}\cdot \hat {\mathbf{e}}^2,\mathbf{\hat{z}}\cdot \hat {\mathbf{e}}^3) </math>
 
The Poisson algebra of these variables is given by
 
<math>
\{ l_a,l_b\} = \epsilon_{abc}l_c, \  \{l_a, n_b\} = \epsilon_{abc}n_c, \ \{n_a, n_b\} = 0
</math>
 
If the position of the center of mass is given by <math> \vec{R}_{cm} = (a \mathbf{\hat e}^1 + b \mathbf{\hat e}^2 + c\mathbf{\hat e}^3)</math>, then the Hamiltonian of a top is given by
 
<math>
H = \frac{(l_1)^2}{2I_1}+\frac{(l_2)^2}{2I_2}+\frac{(l_3)^2}{2I_3}+ mg (a n_1 + bn_2 + cn_3),
</math>
 
The equations of motion are then determined by
 
<math>
\dot{l}_a = \{ H, l_a\}, \dot{n}_a = \{H, n_a\}
</math>
 
==Euler Top==
 
The Euler top is an untorqued top, with Hamiltonian
 
<math>
H_E = \frac{(l_1)^2}{2I_1}+\frac{(l_2)^2}{2I_2}+\frac{(l_3)^2}{2I_3},
</math>
 
The four constants of motion are the energy <math>H_E</math> and
the three components of angular momentum  in the lab frame,
 
<math>
(L_1,L_2,L_3) = l_1 \mathbf{\hat e}^1 +l_2\mathbf{\hat e}^2+ l_3 \mathbf{\hat e}^3.
</math>
 
==Lagrange Top==
 
The Lagrange top is a symmetric top with the center of mass along the symmetry axis at location, <math> \vec{R}_{cm} = h\mathbf{\hat e}^3</math>, with Hamiltonian
 
<math>
H_L= \frac{(l_1)^2+(l_2)^2}{2I}+\frac{(l_3)^2}{2I_3}+ mgh n_3.
</math>
 
The four constants of motion are the energy <math> H_L</math>, the angular momentum component along the symmetry axis, <math> l_3</math>, the angular momentum in the z-direction
 
<math>
L_z = l_1n_1+l_2n_2+l_3n_3,
</math>
 
and the magnitude of the n-vector
 
<math>
n^2 = n_1^2 + n_2^2 + n_3^2
</math>
 
==Kovalevskaya Top==
 
The Kovalevskaya top <ref name = "kovalevskaya"/><ref name = "Perelemov"/> is a symmetric top in which <math> I_1=I_2= 2I_3=I</math> and the center of mass lies in the plane perpendicular to the symmetry axis <math>\vec R_{cm} = h \mathbf{\hat e}^1</math>.   The Hamiltonian is
 
<math>
H_K= \frac{(l_1)^2+(l_2)^2+ 2 (l_3)^2}{2I}+ mgh n_1.
</math>
 
The four constants of motion are the energy <math> H_K</math>,  the Kovalevskaya invariant
 
<math>
K = \xi_+ \xi_-
</math>
 
where the variables <math>\xi_{\pm}</math> are defined by
 
<math>
\xi_{\pm} = (l_1\pm i l_2 )^2- 2 mgh I(n_1\pm i n_2),
</math>
 
the angular momentum component in the z-direction,
 
<math>
L_z = l_1n_1+l_2n_2+l_3n_3,
</math>
 
and the magnitude of the n-vector
 
<math>
n^2 = n_1^2 + n_2^2 + n_3^2.
</math>
 
==References==
{{reflist}}
 
[[Category:Hamiltonian mechanics]]

Latest revision as of 21:36, 16 October 2014

If you like the "Canadian Belt Knife" by cold steel (which is created in Taiwan) I would suggest that you genuinely owe it to oneself to check out the original. Welcome to my site! My name is Lucas Bullington, I produced just about every one of the knives you will see in the pages of this web page. Please take pleasure in the pictures, bookmark this site and check back normally.



The class act in rod-guided systems is the EdgePro Apex Sharpening Technique. Ben Dale, the owner of EdgePro, has spared no expense in his pursuit of excellence in hand sharpening. The Apex is rugged and utilizes comparatively huge 1 x six inch aluminum oxide waterstones. The angle guide is constantly adjustable for any angle from 10 degrees to over 25 degrees. My measurements confirmed that the angles had been exactly as marked. The Apex comes with a excellent instruction book.

Due to the hinge pin, no folding knife is as powerful as a fixed blade knife. I as soon as broke the hinge pin in a Buck Folding Hunter by (stupidly) hammering on the back of the blade with a piece of wood. Folding knives are not my selection for separating the ribs from the breastbone or splitting the pelvic bone. Otherwise, they are fine and I practically normally carry a single in the field. The Buck 110 Folding Hunter blends all of these characteristics into a single amazing knife. With its locking mechanism, stainless steel clip-point blade, and iconic legacy, this knife ensures that durability, efficiency and security will be practically assured when making use of this knife. This knife also comes in at a pretty budget-friendly price despite carrying all of the functions suggested!

Start off by cleaning any residue that may possibly be on the blade. Take a whetstone that has been soaked in water for about 10 minutes. The face side of the blade should really be about 1/eight inch more than the stone. Make sure you do not cut into the whetstone with the sharp cutting edge of the blade. At a 15-20 degree angle, slide the blade back and forth more than the stone evenly and speedily until the blade is sharpened. Turn the knife over and repeat these measures. You can sharpen most knives employing this strategy. How to Hone Your Knife.

To commence, ask yourself, "How do I intend to use this knife?" If you happen to be searching for a knife that will carry out one particular precise task well — skinning a deer, for instance, or cutting branches around your hunting stand — then you could want to choose a specialty knife created with a single unique objective in thoughts. On the other hand, if you acquire a specialty knife to use as a multi-objective tool for backcountry camping, it likely will not carry out several of the tasks you may have to have it for. Normally start out the choice procedure by picking out a style that's very best suited for the chores the knife is intended to deal with.

Ring Lock – Although you may possibly not see as many ring locks, they are still extremely simple to use and sturdy as a locking mechanism. It differs in that you twist a ring if you want to open the knife. When the ring is twisted the knife can be folded into the gap and locked by twisting additional. Then to close the blade just do the opposite by twisting the ring folding the blade down and twisting but again. They were well-liked among makers for their affordable expense in making the ring lock.

These are the upper echelon of knives for several, and are recognized for getting quite high quality blades. Spyderco has worked for years perfecting the ergonomic design and simplicity of their models, giving a clean, functional feel to numerous of them. These practices have endeared the organization to those who rely on their knives in survival scenarios or emergencies such as members of the military, law enforcement, and even some emergency medical teams. Click Here for Full Pricing, Ratings and Testimonials Fixed 3.six four.9 8.5 2.7 4116 German stainless steel Thermo plastic $ four.7 Kershaw 1605 Clash Folding Knife with SpeedSafe Stainless steel – do not rust. Even so, its composition makes it susceptible to denting and other forms of deformation from pressure when sharpened Should you have just about any inquiries concerning where by along with how to employ Schrade Knives, you are able to e mail us on our own web site. .