Questions tagged [dynamics]

Questions about the dynamics of a system. Currently there is a very large scope ranging from from dynamics in mechanics, vehicle and flight dynamics, to system dynamics and fluid dynamics.

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29 views

How is rack and pinion steering configured for different wheel/axle spacing?

The rack and pinion is supposed to turn each of the front wheels differently, such that lines orthogonal to the wheels will intersect in line with the rear axle: Which components of the rack and ...
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31 views

Why is the sum of binormal forces equal to zero?

I've read in Hibbeler Dynamics, page 131, that when considering a coordinate system with normal and tangential axes, the sum of binormal forces equals zero. I don't understand why this is true, maybe ...
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Modeling rigid body dynamics: Trouble with equations, encountering nonsense answers

Hi, I am working on modeling a simple rigid body dynamic system through a certain range of motion. Here is the picture of the system. I am trying to solve the system for the variables $x_1'', y_1'', ...
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Plane Wave Expansion method

I have very recently ventured into the domain of periodic structures. In the literature, I came across the Plane Wave Expansion method to compute the dispersion curves. I managed to code it in 1D . ...
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1answer
57 views

How do rollercoaster designers calculate the ideal curve?

I've been looking into rollercoaster track designs and wondered how they mathematically calculate the ideal curves to fit some specific layout without creating excessive Gs or other rider discomfort ...
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1answer
56 views

Free body diagram of a differential-drive mobile robot

I'm trying to study the free body diagram of this differential-drive mobile robot in case of straight trajectory (same torque applied on both of rear wheels) and pure rolling motion I started ...
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86 views

is a positive acceleration indication that velocity must be positive?

the question is clear and straight forward but when i get the velocity it should be ±√2 what i don't understand is the guide answer refusing the -ve value because acc is always +ve thank you in ...
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1answer
52 views

Determine the minimum horizontal force to disturb the equilibrium

Three blocks of 1N 2N and 3N are placed one over the other respectively. If the friction between the topmost 1N and the middle 2N block is twice the friction between the lowest 3N and floor then ...
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22 views

Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle

My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
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42 views

How to get the normal acceleration

For the problem below, I tried solving it, but I don't know where I should get the value of normal acceleration, guess I was lost. And here's what I solved so far
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80 views

Why does my trimmer feels heavier when it is operating and its fully charged?

I have a Philips trimmer which when fully charged feels much heavier than when it is not charged. Also , the blades move much faster when it is fully charged I.e it’s weight , speed of blades kind of ...
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Input signal rescaling block [closed]

The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown. The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
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Find a constraint relation for this Q of 3 pulleys and 2 blocks attached with string

Using any method find the constraint relation between mass 1 and mass 2. Assumptions: No friction , massless string and pulley. Q: Find constraint relation between 1kg and 2kg block. what I tried so ...
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How do engineers reduce vibration of system with multiple known natural frequencies? How do they design the isolation system for specific frequencies?

I have a system that is pretty much a chamber that needs to sit on the ground. I measured the transmissibility of the chamber vs the ground (output/chamber acceleration over input/ground acceleration) ...
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1answer
37 views

Trajectory of the center of mass of a vehicle

The problem is to find the trajectory of the center of mass of a car when it is rotating and translating (after an off center collision, for instance) What i know as input is the trajectory of the ...
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1answer
29 views

Conceptual question about rotational and translational kinetic energy

My real life problem is to calculate initial translational and angular velocities of a vehicle in a loss of control to a stop. (The vehicle will translate and rotate about it's center of mass.) ...
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47 views

Are equilibrium values of a differential equation uniquely dependent on its constants?

I have a dynamic model which undergoes two distinct stages. The system starts out with certain initial conditions and once a specific point is reached in stage 1, these ending conditions are used as ...
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25 views

Velocity and Acceleration Polygons for Mechanism

I need to determine the velocity and acceleration of point H using vector equations and drawing a polygon. Given data is shown. $\omega$2 is 5.8 rad/s and $\phi$2 is 120 degrees I know how I can draw ...
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110 views

Reaction force at a pin joint for a rod that is rotating about a fixed axis

In this diagram, assuming there is no friction between the pin joint and the rod, I understand that the rod will rotate about $O$. However, let's say that the rod is released from $ \theta = 0$ and ...
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1answer
35 views

Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance

Suppose a system is described by the following ODE: $$\dot{x} = f(t,x)+u$$ where $x$ denotes the state of the system $f(x,t)$ is an unknown nonlinear function which meets the following condition: $$ ...
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Find orientation of reference nodes in Abaqus

I am constructing a simplified model of a pontoon-supported floating bridge in Abaqus. I have chosen to represent the pontoons as one-noded user-elements defined from the mass and stiffness matrix for ...
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1answer
74 views

Angular acceleration of the CD bar

Determine the angular acceleration of the $CD$ bar for the situation illustrated in the figure. The solution is $474 rad/s^2$ $counterclockwise$ I've done: $v_B = v_A + w *r_{AB} <=> v_B= -3j$ ...
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2answers
67 views

Fault Recovery of a UAV using MATLAB

I'm currently investigating fault recovery in a UAV using MATLAB. I've been given several variables: phi = the roll angle psi = the yaw/heading angle beta = the side slip p = roll rate r = yaw/...
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1answer
52 views

Proof of angular velocity identity

I've been going thru the book by Hodges and Roithmayr regarding dynamics theory and I can't seem to prove that: I have tried using multiple substitutions, including the fact that every component of ...
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1answer
25 views

why do we need state feedback in H-infinity concept instead of output feedback

I have faced control of a flexible manipulator which have a zero dynamic related to flexible parts dynamic. the zero dynamic states (generalized states) are not observable in input-output dynamic and ...
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Linearisation of the Equations of Motion of an Inverted Double Pendulum

I am working to develop a deep reinforcement learning model for balancing an inverted double pendulum. To do so, I needed to derive the equations of motion, via the Euler-Lagrange (EL) method and now ...
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1answer
42 views

Pulley with mass dynamics question

A pulley system has mass moment of inertia of 1.4kgm^2. If 8kg block is released from rest from S=1, by using energy approach what is angular velocity at S=2? Radius of pulley is 250mm. Note S is from ...
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37 views

Angular Acceleration

Need confirmation for this question please: A pulley with Radius of 90mm and a mass moment of inertia 0.28$kgm^2$ about its central axis is subjected to a torque of 50Nm about this axis. What is ...
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42 views

Condition for equilibrium of a rigid body on a horizontal surface

The following question is from a past paper from Further Mechanics and it has been bothering me immensely I have spent hours cracking at a way to make sense of it, the question is in two parts Part ...
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55 views

Mechanics Dynamics Question

Alright so this is my question lasses and lads: a disc with a mass moment of inertia 0.125kgm^2 about its central axis is rotating at 180rad/s about the axis. What is the angular momentum of the disc ...
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Sprocket Angular Velocity [duplicate]

I have a question please that I need help on. Consider the chain that is draped over the sprocket with mass moment of inertia of 0.005kgm^2 about central axis. If 4kg block is released from rest from ...
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32 views

Are there examples of spring-mass-damper system that exhibit increasing growth in an unstable way

Simply, are there examples of spring-mass-damper systems that exhibit unbounded behavior or at least increasing behavior for a period of time. I am trying to do some vibrations research, but I am ...
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153 views

Force and the reactions on the supports

Consider the movement in the vertical plane of an $AB$ bar with a mass of $20 kg$, $0.8 m$ long and supported by two cursors: one at the end A and the other at point G coinciding with the center of ...
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Is controlling humidity more precise when calculating with relative or absolute humidity?

I have a tubing system where I need to precisely control relative humidity. All my sensors are giving me temperature [°C] and ...
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1answer
81 views

Determine the aceleration of points B,C and D, angular aceleration of rod and the tension in rope DE when ropes AB suddenly breaks

The solutions are F(DE)=134.38N, a(D)=2.016m/s^2 , α=1.29rad/s^2, a(C)=7.828m/s^2 I agree that the FBD and the KD are these: Then to solve this problem I've done: $$\sum M_{c}= I \alpha_{BCD}$$ $<=...
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39 views

How to find the speed of a boat needed to become airborne on a wave

I am doing a small dynamic project that needs to predict the boat's (boat with propeller) movements in a wavy sea condition as shown below: as the boat is at the peak of the wave, how to determine ...
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1answer
43 views

Determine Stiffness (k) and Mass (m) of a system from impulse response

I have a test sample (Piezo Diaphragm) which I am actuating with a voltage supplied to the sample to assess the impulse response. When this voltage is supplied to the sample a deformation per unit ...
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Shell Breathing Modes and Base Excitation

I have been reviewing "Vibration of Continuous System" by S. Rao as part of self-studying to help with work. I started reviewing the chapter regarding shells and noticed that shells have ...
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How are circular dependencies dealt with inside MBSE?

How are circular dependencies (best) managed inside of MBSE environments? Let's say I have two properties that are linked to each other / they are linked to properties that affect each other. How is ...
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What is the order of execution in system models?

I'm learning SysML/MBSE right now. In what order is a model "executed", that is: in what order are dependencies between properties reconciled? For instance, if I have one component/subsystem ...
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1answer
55 views

If aboard a train being driven along a track by centripetal force, would it feel like you were on a regular straight track?

Question: If aboard a train being driven along a track by centripetal force, would it feel the same as if you were on a regular straight track? I hope this isn't subjective, I think there is a right ...
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1answer
185 views

Determine the angular velocity and angular acceleration of the AB bar at the instant shown

Consider a sliding cursor C that is fixed to the disk which has a constant angular velocity counterclockwise at 4 rad/s. Determine the angular velocity and angular acceleration of the AB bar at the ...
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1answer
72 views

How to determine the angular velocity of the platform as a function of motor rotations per second?

Hello all of you engineering geniuses. Awhile ago a very talented individual on here helped me work out the conceptual mechanics of this design. As you can see from the model, there is a lead screw ...
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2answers
45 views

Damp vibration on phone attached to car seat

I'd like to create a 3d printed system to damp the vibrations on the phone when we are on the road. The idea is to be able to hold the phone for my little kid when we travel First I tried a spring ...
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1answer
42 views

Why is longitidunal force of tyre calculated negative in SIMULINK?

With the help of the Vehicle Dynamics Blockset of SIMULINK, it is easy to obtain longitidunal force (tractive force) of tyre by some of inputs. You can see one of examples below. In this simulation, ...
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196 views

Degrees of Freedom for Complex Pulley Systems

I'm trying to understand DOF clearly, but this pulley system has me doubting myself. When I try to determine the degrees of freedom, I sum the DOF of each object, and subtract the constraints. for ...
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1answer
23 views

Moment placed off-centre on a rotating body

Imagine a body which is allowed to rotated around its centre of gravity. I place a rotating moment, $M_d$ on a point which is a distance d from the body's centre. $M_d$ is only required to put the ...
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37 views

how do i keep static deflection in a spring at a minimum upon applying gravity in a mass spring system without altering the response?

i modelled a simple mass spring damper system (with a vertical orientation) with base excitation in solidworks. After applying all necessary parameters, i plotted responses with and without gravity ...
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Gear/Mechanics problem: How to design to allow for 2 types of rotation

I am designing a new mowing system that can effectively mow around poles. The machine consists of an arm that is attached to the back of a tractor and runs off its PTO. At the end of the arm is a ...
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1answer
54 views

Is the relative acceleration with respect to a translating frame equal to that with respect to a fixed one?

My book, written by Beer, states that the rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in translation. But while it says the derivative ˙rB/A ...

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