Click here to go to the applet.
This javascript applet is a simulation of a symmetric top with one point fixed. When the applet starts,
you will see the top spinning around one of its principal axes with a small initial tilt. Its rotation
axis is also rotating slowly around the vertical, which is called precession.
The angle of tilt is also changing slightly, which is called nutation, but that is
small and quickly damped out on the default settings.
The Example popup lets you select some other examples like:
- tops nutating with various patterns
- a top with no gravity, showing how the Ω vector precesses around the angular momentum vector
- four masses attached to a massless rigid support
- a gyroscope
- a bike wheel with the axle hanging from an invisible support
- a tippe top
Reset resets the top to its initial conditions.
The top traces out a yellow line as it moves showing its path. Clear Trail erases the yellow line.
Zoom In and Zoom Out adjusts the view, or you can use the mouse wheel.
Reverse Spin reverses the direction the top is spinning.
Apply Torque applies torque to the top in the specific direction, as long as the button is held down. The
Torque Strength slider adjusts how strong this torque is. You might want to slow down the simulation before
applying a strong torque.
Simulation speed controls the speed of the simulation, which is in real time by default.
Spin speed controls how fast the top is spinning.
Initial tilt controls the initial tilt angle. Whenever you change the slider, the top will reset to its new initial conditions.
Gravity controls how strong gravity is. By setting it to zero, you can turn it off altogether.
Damping controls the amount of friction. The top's spinning motion is not damped, but rotation along other axes is damped.
If the Tippe Top is selected, then damping works differently. Then there is friction at the contact point between the top and the floor
which damps rotation along all axes.
The Stopped checkbox stops the simulation.
The Show Velocity checkbox shows the velocity of the edge of the top at several points.
The Show Ω Vector checkbox shows the normalized direction of the rotation vector. It doesn't show the magnitude, because as you change
the spin speed, the arrow would often be too large or too small to be practical.
The Show Angular Momentum checkbox shows the direction of the angular momentum vector. You may not be able to see the angular momentum and omega vectors
at the same time because they may be too close together.
The Show Gravitational Torque checkbox shows the direction of gravitational torque.
The Show Trail checkbox shows the path of the top.
The Solid Floor checkbox can be turned off to make the floor drawn as a transparent wireframe. This may happen anyway if there is a vector
being displayed under the floor. The top is free to move through the floor, whether or not the floor is drawn as solid; we don't attempt to simulate
the top's collision with the floor.
The Texture popup controls the texture used to draw the top. By default, a high contrast texture is used so you can clearly see the
rotation. But if that is giving you a headache, you can change it to "Solid Color".
The applet also displays:
- elapsed time (also showing how much faster/slower it's running than real time)
- the angular speed around the spin axis (in the body frame)
- gravitational acceleration
- the average precession period
- the tilt angle
- the precession angle
The bike wheel model is from Free3D.com but the original is much better.
I decimated it down quite a bit to make the file smaller.
Thanks to Aaron Boman for the obj file loader. Copyright (c) 2013 Aaron Boman and aaronboman.com
Thanks to the authors of gl-matrix.js. Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.
Click here to go to the applet.
java@falstad.com
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero’s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ‘Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?’ ‘I have no scruples on that point,‘ replies the impatient poet. ‘But I have,’ rejoins Fuscus,—‘a little weak-minded, one of the many, you know—excuse me, another time.‘331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.’332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff’s hand was quietly coming down. “What happened to you?” begged Sandy. “Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn’t come back, I thought I’d better go and find you—and see if it meant anything to you.” She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm—foreign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do—I can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident—wud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion—fireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England—France. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently.