Tagged Questions

Questions relating to Newton's Laws of Motion

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Attitude dependence on orbital elements

How would errors in the argument of perigee affect attitude? Is there a general approach documentation? Thanks
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The position of a point mass that moves in a straight line .. / Determine the units

The position of a point mass that moves in a straight line is given by $x(t) = At^2 + Bt + C$, where $t$ is time. Determine the units of $A$, $B$ and $C$. The answer to the question is [A] = M/S^...
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Elastic Body Simple Deformation

In continuum mechanics we can consider a reference frame $B = [0,1]$ along with a homogeneous deformation $F$ where $x = Fp$ for $x \in \mathbb{R}$ and $p \in [0,1]$ and $F = 2$ so $F[B] = [0,2]$. ...
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Bead on rotating hoop with mass, determine the lagrangian

"Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop free to rotate about ...
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Why don't we differentiate velocity wrt position in the Lagrangian?

In Analytic Mechanics, the Lagrangian is taken to be a function of $x$ and $\dot{x}$, where $x$ stands for position and is a function of time and $\dot{x}$ is its derivative wrt time. To set my ...
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A criterion for area preserving dynamical system

In my investigation of dynamical systems I was met with this seemingly easy question I could not find an answer to: If we have a two dimensional system of autonomous ODEs viewed as a 2D dynamical ...
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Difficult projectiles question

A particle $P$ of mass $m$ lies on a plane inclined at an angle $\alpha$ to the direction vector $\mathbf{i}$. At $t=0$ the particle is projected from the origin of the coordinate system with speed $U$...
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This is a rod attached to a wall by a light inextensible string: And here is a diagram showing the forces acting: I want to find the normal reaction $R$ between the rod and wall using moments ...
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I did a Maths question on mechanics using calculus and physics students disagreed, why are the solutions different? [duplicate]

So, I did the following question and got 2 different answers. Question: A lighthouse located 300 metres from a straight shoreline sweeps its beam of light around in a circle at a constant rate of 1 ...
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About periodic trajectories of a Hamiltonian system

Consider a Hamiltonian system with Hamiltoniana $H (\mathbf{q}, \mathbf{p})$, where $H$ doesn't depend on time $t$. It is known that in some domain of phase space the trajectory of system are peiodic. ...
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Compute the following line integral along a path of your choice (Finding potential)

Consider the following vector field: $$\vec A(x,y,z)=(yz)\hat i+(xz)\hat j+(xy)\hat k$$ Compute the line integral of $A$ along a path of your choice connecting $(0,0,0)$ to $(1,1,1).$ I recognise ...
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Conservation of Net Mechanical Energy in SHM

I have a question I wish to answer: Show that the simple harmonic motion solution of the simple pendulum in the form $$\theta (t) = A\cos ({\omega _0}t)$$ (constant A) conserves net mechanical energy ...
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A soft question on Gauge Equivalence in Integrable Systems

I have a question about two well-known spectral problems in Integrable Systems. These are the Dirac and the ZS-AKNS spectral problems. They are are known to be gauge equivalent (please see equations (...
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Calculate Universal Time for when an object in orbit reaches a given radius / altitude?

Assuming that an object in orbit WILL reach a given radius / altitude at some point in the future, how can I work out the exact time it will reach that point? Assume that the object is a Satellite in ...
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Why is $\omega$ the natural/angular frequency?

Pardon me cause I'm a little confused. If we have something like: $y=A\sin \left( \omega t-\delta \right)$ why would $\omega$ be considered the natural frequency? I always thought the frequency of a ...
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Finding stagnation points and stream function

Sorry for the lack of latex. The question I want to ask would need all this info and it would take very long to write it. (a) Irrotational flow means $\nabla \times \textbf u =0$ so we can define ...
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Viscous fluid boundary condition

Consider an incompressible viscous ﬂuid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The ﬂow ...
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Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
We have $\omega = (0,0, \xi(x,y,t))$ and $\textbf u =(u(x,y,t),v(x,y,t),0)$ and that $$\frac{\partial \xi}{\partial t} +u \frac{\partial \xi}{\partial x} +v\frac{\partial \xi}{\partial y}=0$$ is a ...