All Questions
13 questions with no upvoted or accepted answers
2
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answers
80
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Equation of Motion of Rigid Body Represented by Twist and Derivative of Twist
This question is an extension of question Understanding terms Twist and Wrench.
Assuming there is a rigid body with body twist denoted as $\mathcal{V}_{b}=\left(\boldsymbol \omega_{b}, \boldsymbol v_{...
- 21
2
votes
0
answers
183
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Proving that the relative angular velocity of any particle with respect to any other particle is the same in a rigid body
Claim: The angular velocity of any point mass of a rigid body relative to any other point mass is the same, i.e., $\vec{\omega_{i,j}} = \vec{\omega}\;\,\forall{i}\,\forall{j}$, where $\vec{\omega}$ is ...
- 41
2
votes
4
answers
1k
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Uniform Circular Motion w/ Tension and Friction
So I had a problem today which I couldn't make any sense of. I don't have access to it at the moment but this is a pretty accurate approximation.
Basically, a mass (m) is swinging horizontally on ...
- 21
1
vote
1
answer
59
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Statistical Analysis of motion under central force
My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
- 11
1
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0
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136
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Difference between eigenvalues of the potential energy Hessian vs. "generalized" eigenvalues with respect to a kinetic energy "metric"
Simple version
Consider if we have a Lagrangian defined by
$$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$
where the potential energy $U(q)$ has a single minimum at $q=0$ (...
- 3,780
1
vote
1
answer
153
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Finding The Trajectory of particle Kept on a rotating surface
Suppose we "Keep" a particle on a circular, rotating turn-table, rotating with constant angular velocity $\dot{\theta}$, (i.e, the at $t=0$,when the particle makes contact with the table, the ...
- 1,325
1
vote
1
answer
76
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Determining acceleration in order to meet a space-time-velocity reservation
An Example
A train on a single line track is told to be at position $x_{res}$, at time $t_{res}$, and to be moving at exactly $v_{res}$ when it hits that point. Where $_{res}$ denotes the reservation....
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1
vote
0
answers
101
views
Move body in 1-dimension to desired state by applying force
Consider a simple point mass of $M$ in vacuum in 1-dimension with initial position $x_0$, velocity $v_0$ and acceleration $a_0$. Our goal is to move this body to position $x_1$ with velocity $v_1$ and ...
- 505
0
votes
1
answer
98
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Angle, and maximum area of projectile motion accounting air resistance
Recently I was wondering about what will happen to the particle when subjected various elevation angle of projectile motion if we account air resistance. I want to know what the angle of elevation ...
0
votes
0
answers
73
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Necessary and sufficient conditions for periodic motion
Let us fix a reference frame $S$ with origin in $O$ in the euclidean space $\Bbb R^3$, then let us also define a periodic motion in the following manner:
A motion is periodic if and only if the time-...
- 402
0
votes
1
answer
91
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The velocity of an object leaving the inclined plane
I saw the question below in our physics textbook. It asks
A block of mass m is released and slides down on the frictionless inclined surface ( the inclined plane is of concrete and doesn't ...
- 221
0
votes
2
answers
70
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What is the direction of linear motion after this impact?
I've been thinking about a situation where I am not sure what the resulting motion would be.
This is what I am thinking,
1) P is the point of application of force. If there are two force components ...
- 11
0
votes
1
answer
78
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circular(ish) motion?
how would one describe as a function of time the position vector of an object with initial position $\vec{x_0}$ and velocity $\vec{ v_0}$ experiencing a central force of constant magnitude around the ...
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