Mathematics Stack Exchange
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Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

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Kinetic energy of system is homogeneous quadratic function of generalised velocities $\dot q_i$

According to Hamilton's equation....the relation $$ 2T = \sum_ip_i\dot q_i $$ is obvious. But How would I show that kinetic energy is homogeneous quadratic function of generalised velocities $\dot q_i$?
user609389
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Find magnitude and direction of resultant of three given forces?

Using this diagram: A hot-air balloon is ready for take-off. The diagram shows the balloon, tethered by two ropes AB and CD, reach attached to the balloon and the horizontal ground. The weight of the balloon is 3000N. The tensions in AB and CD are…
user61400
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Modify formula for bouncing object to increase restitution

I originally started a thread over on Stack Overflow about this but it's diverged into mathematics which is way beyond my understanding. Basically I have the following formula (it's JavaScript but I don't think it should really matter) that…
Briquette
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Algebraic Speed Distance And Time Question GCSE

Question: What I did: $x$ = miles $\frac{x}{60mph}$ and $\frac{x}{45mph}$ and so $x = 60t$ and $x = 45t$ I don't know what to do from here to work out time. Thankyou, any help is appreciated!
xx_Gcsemathstudent_xx
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Calculation of impulsive tension and velocity

can anyone please help with the setup of a question. Firstly, here is a similar question just to show the style of the solution expected: And so the analysis continues. So I am trying to set up a similar pair of diagrams for the following…
gnitsuk
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Lagrangian Equation

A hoop with radius r is rolling, without slipping, down an inclined plane of length l and with angle of inclination 'a'. Assign appropriate generalized coordinates to the system. Determine the constraints, if any. Write down the Lagrangian equations…
Sharmi C
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Metal frame pool pressure calculation

I'm not sure this is the right place to ask this question, but I have a real life problem that requires calculation and I do not have the math knowledge to make them myself. I have an above-the-ground pool, with dimensions of 2x4 meters and water…
Dimkin
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Find the least possible value of U^2?

QS:A particle P of mass m is connected to a fixed point O by a light inextensible string OP of length r, and is moving in a vertical circle, centre O. At its lowest point, P has speed U. When the string makes an angle α with the downward vertical it…
Powerful blaster
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Central forces problem: find radius R

A particle of mass $m$ moves in two dimensions in a potential $V(r)=\frac{1}{2}\left(\frac{\alpha}{r^2}+\beta r^2 \right)$ where $r$ is the radial distance from the origin in polar coordinates, and $\alpha$ and $\beta$ are positive constants. I have…
apt98
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Minimum speed of conical pendulum connected by two strings

Question: A particle P of mass 2.5kg is attached to fixed points A and B by light inextensible strings, each of length 50cm. A and B are 96cm apart with A vertically above B. Particle P moves in a horizontal circle with centre at thr midpoint of AB.…
owenhu99
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Doubling your velocity

Suppose you were to run one lap around an olympic oval with a given distance $d$, over time $t$ with velocity $v_1=d/t$. For your second lap, how fast must you travel so that your average velocity across both laps is twice your velocity during the…
John Glenn
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Can I use angular diameter to determine the apparent size of an object at a given distance?

I believe this question uses Angular Diameter to determine the answer but I'm not sure how to use it. Question: If a widget is 10 meters wide and it is positioned 1,000 meters from the observer how wide will it appear? Alternate Equation: At…
DR01D
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How to solve $-\frac{1}{2}gt^2\sin \theta=x$ when $x$ equals $0$

This given equation, $-\dfrac{1}{2}gt^2\sin \theta=x$ should describe the path of a ball rolling up an incline with initial speed $v_0$. The question is: how long will the ball take to return to its starting point? It is obvious that the equation…
Math420
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What does the phrase "in the sense of $\theta$ increasing" mean?

I've encountered this phrase many times while doing problems in dynamics. It appears when I am trying to write a vector equation using scalar quantities and almost always a derivative is involved. I don't have a clear idea on this. Some explanation…
Not Euler
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Why is the angular momentum of a rotating body the same about any point on its axis of rotation?

The angular momentum of a rigid body is defined with respect to an origin. But when the body rotates about an axis we define it with respect to the axis; as if it would be the same about any point on the axis. But why would it be the same?
Not Euler
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