Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [kinematics]

For questions on the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

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The vertices of an equilateral triangle are shrinking towards each other

For an equilateral triangle ABC of side $a$ vertex A is always moving in the direction of vertex B, which is always moving the direction of vertex C, which is always moving in the direction of vertex A. The modulus of their "velocity" is a…
kuch nahi
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Is there a better notation for integrating twice?

I'm studying kinematics with varying acceleration. To calculate the displacement from the acceleration you have to integrate the acceleration with respect to t, then integrate that with respect to t, this time with limits. I've been writing…
Tim
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How to generalize the Euclidean "unicycle" model?

There is a common system of ODEs known as the unicycle model / Dubin's model which describes the kinematics of an ant-like "unicycle" that can drive forward with some velocity $v(t) \in \mathbb{R}$ and turn in-place with some angular velocity…
jnez71
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Movement time of object with constant jerk, limited acceleration and velocity

A product is initially at rest on a conveyor belt: The initial conditions of the product can be described as follows:$$x_i=0$$ $$v_i=0$$ $$a_i=0$$$$j_i = j⋆ $$. The product will be moved forward distance of exactly Δx (known) to position it under…
Luminaire
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Integrating product of Dirac deltas and step functions

I have the following integral $$\int d^4\boldsymbol{x}' \,\delta\big[(\boldsymbol{x}-\boldsymbol{x'})^2+\alpha^2\big]\,\Theta(-x_0+x'_0)\,\delta\big[(\boldsymbol{x'})^2+\alpha^2\big]\,\Theta(-x_0'),\tag{1}\label{1}$$ where…
gammadragon
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How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some simplifications here were my hypotheses: The plane is…
JonHerman
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Is displacement the change in position between two points or is it the position relative to the origin?

The displacement $s$ metres of an object is given by $s(t)=e^{\cos(t)},$ where $0 \leq t \leq \pi$ and the time is $t$ seconds. Determine the displacement of the function at $\frac{\pi}{2}$ seconds. I computed $s(\frac{\pi}{2})-s(0)$ and come up…
BJH
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What's wrong with my formula?

I'm learning about rational functions, and encountered this word problem: A helicopter flies from Vancouver to Calgary a distance of 677km with a tailwind. On the return trip the helicopter was 40km/h slower. The total flying time for both flights…
Neil Judi
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a cyclist travels 30 km in one hour

a cyclist travels 30 km in one hour 1) Demonstrate that there is an interval of 10 minutes such that the cyclist has traveled 5 Km 2) Is there always a time interval of 40 minutes during which he will have traveled 20 Km? for the first question,…
LeFo
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How to solve equation of motion for multiple pulleys

Find the acceleration of any mass for this type of system. At the lowest pulley there are two masses connected, $m_n$ and $m_{n'}$. I having a hard time tackling the finite problem but the solution as $n->\infty$ should be easier. For $m$ is a…
jg mr chapb
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Are Position and Velocity (or Velocity and Acceleration) Vectors Always Parallel?

While reading Chapter 1 of an astrodynamics textbook, I came across the statement: $$\mathbf{v}\cdot \mathbf{{\dot{v}}}=v{\dot{v}}$$ In other words, the dot product of velocity and the time-rate-of-change of velocity is simply equal to the product…
Bryson
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Matrix exponential of the sum of two skew-symmetric matrices

This is my first message in this site. I'm a mechanical engineer with, amongst others, an interest in inertial navigation. I'm currently reading the book "Principles of GNSS, Inertial and Multisensor Integrated Navigation Systems" from Paul D.…
Guillermo Benito
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Deriving the kinematic equation $v^2=v_{0}^2+2a(x-x_{0})$.

I have a question on deriving the kinematic equation $v^2=v_{0}^2+2a(x-x_{0})$ from first principles and the known kinematic equations. Is this simply differentiating, but with respect to time($t$)? If so, wold the process be ($a$ is a constant)…
Kenshin
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Find Square Size From Inscribed Triangles

I am working on a robotics calibration problem and I've run into a geometry problem that I'm sure has a solution, but I'm not sure how to tackle it. We have a square and we want to find the size of the square. We know the lengths of BE, CE, and DE.…
Bar Smith
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Launch angle of projectile motion not in terms of time

I have these two projectile-motion equations: $$ vt\cos(\theta)=d $$ $$0=h+vt\sin(\theta)+\frac12at^2 $$ Is it possible to derive an expression for $\theta$ in terms of at most $d, v, h, a$ but not $t?$ The closest I've gotten is $$ t =…
tophatcollection
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