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Why does the ball in Galileo's double inclined plane experiment reach the same height?

Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone ...
Mathologist's user avatar
0 votes
1 answer
53 views

Why for motion planning of quadrators the goal is to minimize the jerk/snap?

In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and ...
Math98's user avatar
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2 votes
1 answer
1k views

Newton-Euler approach for the equations of motion of spherical pendulum attachted to a moving body with 6 degrees of freedom

I would like to obtain equations of motion for a spherical pendulum suspended from a (6 degrees of freedom) moving body (generalization of a simple pendulum on a cart) using Newton-Euler approach. ...
sample's user avatar
  • 23
-1 votes
1 answer
51 views

Question of ball falling down.Difficulty in understanding the formula

A ball is thrown upward from the top of a tower 40m high. u = 10m/s.Find time for it reach AD. g = $10m/s^2$. Taking upwards direction as +ve and downward as -ve. u = +10m/s.$g=-10m/s^2$.s=-40. $-40 = ...
Srijan's user avatar
  • 735
0 votes
1 answer
193 views

Bullet piercing through block problem [closed]

A bullet moving with a velocity of 200cm/s penetrates a wooden block and comes to rest after traversing 4cm inside it . What velocity is needed for travelling distance of 9cm in same block. My though ...
user avatar
0 votes
1 answer
29 views

Velocity of object on extremely low air density?

If we derive velocity in air when setting air resistance to $kv$, we'll get $$v= \frac{mg}{k}\left(1-e^{\frac{kt}{m}}\right) $$ and if air density goes to $0$, $k$ will also goes to $0$. When $t=T$ (...
WienAudience's user avatar
2 votes
2 answers
444 views

Rotation as an example of symmetry in classical mechanics

I modified the question because it was confused. On my book there is this mathematical definition of symmetry transformation: "The equations of motion have a symmetry, if the solutions of the ...
SimoBartz's user avatar
  • 1,978
2 votes
3 answers
281 views

Do the equations of motion have specific characteristics?

I solved a classical mechanics problem in a form somewhat like this: $$x(t)=t^2+5t$$ $$y(t)=t^3$$ $$z(t)=5.$$ The problem asked me to find the equations of motion of an object. From my ...
user7389351's user avatar
1 vote
1 answer
790 views

Control system with equation C = A*x + B*dx/dt

This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place ...
hyperknot's user avatar
  • 167
-1 votes
1 answer
761 views

Laws of Motion: Acceleration to be applied on a free falling object to reduce velocity to 0

Assume that an object of mass 'm' is falling to the earth.The force acting on the same would be F = m*g = 10m (assuming g = 10m/s^2). In this case the velocity of the object at time 't' = 10 seconds ...
Ram Sidharth's user avatar