My problem:
I am trying to find a model, most likely parametric, of the bottom of a swinging carriage of a Ferris wheel. Imagine someone riding in such a carriage swinging back and fourth, creating a pendulum like effect in addition to the rotation of the actual wheel. I am trying to include the rotation of the wheel (cycles/minute), the maximum angle of the swing (the angle from a vertical dropped from the point generated by the swing) and the speed of the swinging (cycles/minute).
What I have:
I have drawn two circles, a large circle being the actual wheel and another that would be traced out if the carriage would only hang without swinging (basically just a copy of the previous circle moved down the number of units that the bottom of the carriage is away from the top of the Ferris wheel). I have x= r cos x ; y= r sin x for the Ferris wheel, but I got stuck there. Then I tried x² + y² = (10)², say, for the wheel and
x² + (y + 2)² = (10)² for the traced circle of the bottom of the carriage, then set x = t to change it to parametric form and solve for y, only I cannot relate the motion of the bottom of the carriage with the motion of the wheel itself, let alone the swinging motion of the carriage. I will describe my drawing. O is the center of the wheel, O’ is the center of the circle generated by the bottom of the carriage as it goes around the wheel. P is the point of the bottom middle of the carriage.I tried drawing a line from both O and O’ to P when the point is at, say, 45 deg in relation to O. I then introduced angles theta and gamma; theta for the angle between OP and the x-axis, gamma the angle from the y-axis and O’P. That’s all I could get.
Sorry I couldn’t actually get a picture. I have no idea where to go from here. I would appreciate anyone’s help on this one, as I don’t even have my name and date on my paper yet. Thank you!
I am trying to find a model, most likely parametric, of the bottom of a swinging carriage of a Ferris wheel. Imagine someone riding in such a carriage swinging back and fourth, creating a pendulum like effect in addition to the rotation of the actual wheel. I am trying to include the rotation of the wheel (cycles/minute), the maximum angle of the swing (the angle from a vertical dropped from the point generated by the swing) and the speed of the swinging (cycles/minute).
What I have:
I have drawn two circles, a large circle being the actual wheel and another that would be traced out if the carriage would only hang without swinging (basically just a copy of the previous circle moved down the number of units that the bottom of the carriage is away from the top of the Ferris wheel). I have x= r cos x ; y= r sin x for the Ferris wheel, but I got stuck there. Then I tried x² + y² = (10)², say, for the wheel and
x² + (y + 2)² = (10)² for the traced circle of the bottom of the carriage, then set x = t to change it to parametric form and solve for y, only I cannot relate the motion of the bottom of the carriage with the motion of the wheel itself, let alone the swinging motion of the carriage. I will describe my drawing. O is the center of the wheel, O’ is the center of the circle generated by the bottom of the carriage as it goes around the wheel. P is the point of the bottom middle of the carriage.I tried drawing a line from both O and O’ to P when the point is at, say, 45 deg in relation to O. I then introduced angles theta and gamma; theta for the angle between OP and the x-axis, gamma the angle from the y-axis and O’P. That’s all I could get.
Sorry I couldn’t actually get a picture. I have no idea where to go from here. I would appreciate anyone’s help on this one, as I don’t even have my name and date on my paper yet. Thank you!