Questions tagged [dynamics]

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Inertial Torque Exerted By Engine on Crankshaft

In Shigley(5th Edition), in Chapter 14. Dynamics of Reciprocating Engine ,Section 14.7 Inertia Forces, the inertia torque exerted by the engine on the crankshaft is given as $$ \mathbf{T}_{21}^{\...
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How do we derive the equation of motion of Cantilever Beam (Euler-Bernoulli Beam)?

I know that the equation of motion of a Cantilever Beam is: $m\frac{{{\partial }^{2}}v}{d{{t}^{2}}}+EI\frac{{{\partial }^{4}}v}{d{{x}^{4}}}+P\frac{{{\partial }^{2}}v}{d{{x}^{2}}}=0$ but how do we ...
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3answers
83 views

Difference between Linear Force and Force about an Axis

I am confused between How forces work when applied in singular linear direction vs Force Applied to a continuous mass about an axis(example to rotate it). Example 1: Consider an object of mass $m$ ...
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2answers
38 views

Kinetic energy of a rigid body

A homogeneous disk with radius $R$ and mass $m$ rolls without sliding on a horizontal fixed plane. Peripheral point $A$ has velocity $v$. Determine the kinetic force of the disk. In my textbook they ...
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34 views

Skew-Symmetric Gain Matrix to Encourage Exploration

I am reading a paper on controls and it has the following snippet: We propose to use the control law $$u_i = K(CV_i − p_i)$$ , where K is a (potentially time-varying) uniformly positive definite ...
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2answers
76 views

Moment equation from dynamics differs with equations from physics & statics. Where did I go wrong?

In my dynamics class, we're being asked to solve the following problem: My Attempt: Since I'm given the initial velocity, final velocity, and distance, I solved for the acceleration of the plane ...
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1answer
21 views

Deformation and stress in moment of hit (Ansys)

This how task goes: i need to find deformation and stress of piston in moment of hit between piston and tool (tool is stationary). Velocity of a piston is (5-7 m/s) and forces are in picture below. I ...
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1answer
50 views

Equation governing relative motion between aircraft and store

I am reading a paper titled Conditions for safe separation of external stores by EE Covert [Link]. In Section 1 Introduction of the paper, the author has given an expression for $d$, the relative ...
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3answers
29 views

How to solve a system of second order ODE from time t = T to t = 0

I have a system of second-order ODEs $$ \mathbf{M\ddot{x} + C\dot{x} + Kx = f} $$ I want to know some good numerical methods to solve this system of the equation given the initial conditions at time $...
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1answer
44 views

Unit Conversion for Mass Density

I am doing a Finite Element analysis of a continuum. In my problem definition I use these units: mm for length, kPa for applied stress, and MPa for material stifness (Young's modulus). With these ...
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0answers
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What is the best way to find solved problems similar to the one at hand?

This is a general question, so sorry if it breaks the rules. However, I think it is very important as more often than not someone else has already solved a similar problem that can be applied to solve ...
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1answer
19 views

Dynamics - Deriving Linear acceleration based on angle theta

Suppose that I am given an equation of some positional vector in the Cartesian coordinate system that is based on some theta shown right below. I am asked to find the linear acceleration based on ...
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1answer
33 views

How to Calculate Torque to Prevent Rotating

I'm stuck with how to calculate the external torque which must be applied to prevent the aircraft rotating about axis? The imagine shows an aircraft which has a jet engine with a rotor that has an ...
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40 views

How to calculate the polar mass moment of inertia

Recently ran into the polar mass moment of inertia when calculating the gyroscopic moments of a rotating shaft. However I hardly find any information about this quantity. Can anyone help me how to ...
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1answer
24 views

What is the relationship between Rotational speed (RPM) and the speed of a drone (Air speed)

I would like to know whats the relationship between these two, is it linear? or what? also i would like to know the mathematical relationship between these two. Thank you
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1answer
39 views

Does the surface roughness play any role in shock absorbing?

Consider a mass of about $130 \pm 10 $ kg, falls from height, let say $2.5 $ m. In order to dampen the vibration and sound, I use silencer or drop pads. I was wondering if introducing the macroscopic ...
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1answer
95 views

Stopping force on wire rope from a falling object

Okay, bit of a weird one. Imagine an object of known mass in free fall, tethered by a wire rope to an infinitely stiff sky hook. When that wire rope eventually tightens, what will be the stopping ...
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1answer
30 views

Elastic waves in very thin plate

Elastic waves in structural elements are described by \begin{align} \rho \frac{\partial^2 u}{\partial t^2} &= (2 \mu + \lambda) \frac{\partial^2 u}{\partial x^2} + \mu \left( \frac{\partial^2 ...
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1answer
130 views

Calculate max deceleration without front wheel slipping (bicycle)

I am trying to calculate the maximum braking force/deceleration for a bicycle. Note: the question assumes only the front brake is used Free body diagram: For dry tarmac where I know there is enough ...
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2answers
32 views

Position vector to Velocity vector

Is it possible to derive velocity vector form position vector without unknown such as: position vector of A = (0.8)i + (1.2)j?
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1answer
33 views

How do I change the coordinate system from x-y to n-t or r-theta by using Matrix? [closed]

How do I change the coordinate system from two dimensional cartesian to two dimensional curve linear and polar by using Matrix?
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0answers
52 views

The optical encoder resolution

The optical encoder has a code wheel with a single track of slots and two photodetectors. The photodetectors are positioned so that they produce signals with a 90 degree phase difference. I want to ...
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1answer
117 views

Motor, a gearbox and a drum with a cable lifting a mass

A lifting device consists of an electric motor, a gearbox and a drum with a cable for lifting a mass. The speed after the initial acceleration is $v=0.5\,\text{m/s}$. The gear efficiency $\eta=0.7$ ...
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1answer
49 views

Moment of Inertia

To calculate the moment of inertia at o, I tried to apply (1/3mq^2) but I am not sure if it is correct. Any help would be appreciated.
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1answer
55 views

Inertial Forces while analysing forces on a Piston in a Slider - Crank Mechanism?

I get that we are analysing the Piston in a non-inertial frame of reference, but the point of my question is that according to D'Alembert's Principle, whenever an inertial force comes in the line of ...
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1answer
54 views

Ball and Socket Wheel Concept

I am sure you all remember those prehistoric computer mouses that had a ball under it. I'm looking for any points and tips on how to create a ball and socket wheel that has an almost frictionless ...
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2answers
46 views

How to calculate traction force w.r.t. rotational speed of a shaft mounted at a certain angle on a surface?

I am designing a new mobile robot platform and i need a generic solution for the robot in order to establish a proper mathematical modeling. My question is about calculation of the traction force of ...
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1answer
18 views

How can I validate the validity of a model of a dynamical system?

I derived a non linear differential equation system for a mechanical system. However I doubt the correctness of it. So I compared the model's dynamics with a VREP simulation. I did this by by Euler ...
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2answers
35 views

Approaches to whether a projectile gets intercepted

Hi everyone, How do I approach questions like part (ii)? From what I understand now, I believe the shortest method is that as long as the ANGLE of the relative velocity of B with respect to velocity ...
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2answers
54 views

Would a plane lift from ground if in a free treadmill?

I was wondering if the force generated from the engines of a jet plane would lift it up from the ground if in a free treadmill. Would it take off?
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2answers
102 views

Dynamic spring tension [closed]

I have rope on a spool that is on a cart that is powered and moving at a constant velocity of 0.5 m/s. The end of the rope is passed thru a break and fixed to the wall. one break has a compression ...
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1answer
113 views

How to model projectile motion using dynamical system matrices

I'm trying to figure out how to model projectile motion which can be defined using a simple [quadratic] equation which defines projectile parabola: $$y = y_0 + v_{0y}t - \dfrac{1}{2} gt^2$$ I came ...
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1answer
58 views

Angular acceleration and the moment of inertia

The wheel is made from a 10-kg thin ring and four 0,5-kg slender rods. If the torsinal spring attached to the wheel's center has a stiffnes $ k = 2 N*m/rad$, so that the torque on the center of the ...
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1answer
45 views

Effect of friction (or horizontal motion) on vertical surface deformation

I am trying to model the dynamics of some system. In summary, the system consists of one horizontal linear actuator that drives an object along a planar surface and one vertical actuator that brings ...
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1answer
30 views

Dynamics work and energy problem

Blocks A and B weigh 30lb and 15lb respectively, and they are both at a height 8ft above the ground when the system is released from rest. Assume the pulley is frictionless. Determine the speed of ...
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3answers
318 views

Resonance vs flutter

Is there any difference between resonance and flutter. Both of them are related to overlap of external excitation frequency and Natural frequency then increase in amplitude even inifite amplitude ...
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1answer
35 views

How to model a driven wheel with no slip

I'm working on a design problem, and I'm having trouble figuring out how to model the torque needed to drive a bike tire at a set acceleration. Let's say I have a tire with normal force between tire ...
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1answer
41 views

Motion of gears [closed]

Gear A and B will have the same speed and tangential component of acceleration at the point where they mesh.why? From plane motion of rigid bodies energy and momentum methods.
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24 views

Frequency domain analysis of steering system of a car

Can anyone share the equations involved, or some relevant theory material for frquency domain analysis of steering rack and pinion using bode plot?
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1answer
77 views

Centroid and toppling [closed]

A uniform block is in the form of a square ABCD of sides 2 m and a unit thickness. E is a point on AD such that ED = xm. The portion EDC is then removed from the block. What is the maximum value of x ...
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1answer
112 views

Calculation of natural frequency in a hinged beam

What I tried: Using the conjugate beam method to find deflection and hence stiffness of the beam, but I am unable to find reactions in the conjugate beam.
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How to run a steady state dynamics, Modal step based optimisation using TOSCA?

What design responses must be given in the TOSCA gui. I chose volume reduction as an objective function with the constraints of displacement. Is this approach correct?
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1answer
422 views

Can a rolling wheel create a side force without first rotating on a vertical axis at its contact patch? [closed]

There is something wrong with the way we describe how a cornering vehicle wheel creates a cornering force. I think a rolling wheel must first rotate on a vertical axis to then create the cornering ...
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1answer
63 views

Pulley question: Which 10N block will accelerate faster?

Background: My professor for system dynamics at my university gave us an engineering dynamics concept quiz. A particular question I am interested in presented two figures I have re-drawn below. The ...
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1answer
93 views

Dynamics of a rigid body in a system of two linear drives

I've been trying to solve the dynamics of this system for quite a while, but cannot seem to get the right answer. I've tried solving it with Lagrangian method but I am not so confident with the ...
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1answer
386 views

Deriving the equations of motion for free-floating spacecraft with a single link robot arm

Note: I had previously posted this question on the Space and Robotics SE sites, but received little/no response. So I've deleted the previous posts and repasted my question here in the hope of ...
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1answer
214 views

Inertia relief in ANSYS - rotating model

I'm trying to use ANSYS to solve statically a dynamic problem. As shown in the image below, there is an orange bar that is constraint to slide horizontally only and attached to another bar (pink) ...
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1answer
57 views

In equilibrium is engine torque zero? Vehicle dynamics

Consider following equations for a driving wheel in a car. $$ J\dot{\omega} = T - F_x R - F_r R \\ m\dot{v} = F_x + F_r $$ where $J$, $\omega$, $T$, $F_x$, $R$, $F_r$, $m$, and $v$ are wheel inertia, ...
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1answer
78 views

Two Dimensional Kinematics

Attempting this kinematics question but not really understanding if what I'm doing is right or completely wrong. Should I be starting by finding Vp? Any help appreciated. Not an assignment, just ...
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1answer
62 views

How are all LTI systems also dynamical systems?

How are all LTI systems also dynamical systems? I understand that LTI systems are linear and time invariant and that dynamical systems describe how one state develops into another, but how would this ...