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1answer
25 views

How to estimate the relative motion using kinematic equations?

Background I am reading the following thesis: Todosiev, E.P., 1963. The action point model of the driver-vehicle system. On page 9 it describes the relative motion between 2 cars as follows:...
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1answer
25 views

What is meant by negative direction of velocity? [duplicate]

What is negative velocity and negative direction of the velocity?
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0answers
9 views

Modeling stilts with equations

I'm trying to make a set of stilts 20 ft in the air that someone could wear to run/jog with, but I was advised that I should first start by modeling the system (user + environment + stilts) in the ...
1
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1answer
68 views

Calculate position with position depending force

I have an equation that says $a(t)= \alpha * s(t)+\beta$ where $a$ ist the acceleration, $\alpha$ and $\beta$ are constants, $s$ is position and $t$ the time. My question is how to get the resulting ...
1
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1answer
69 views

Is it strictly necessary to require gauge invariance of the action and equations of motion?

When writing down an action for a gauge theory, we require that the action be gauge invariant. This is typically taken to mean that the action must be written explicitly in terms of gauge invariant ...
0
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1answer
115 views

Velocity change of air down a cone?

Does the velocity of fluids(specifically gasses) change when traveling down a cone from the wide opening to the narrow opening? If so, is there an equation used to calculate the acceleration or ...
0
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1answer
57 views

Physical significance of omitting a purely time dependent term from a Lagrangian

For a simple pendulum whose point of support moves on a vertical circle of radius $a$ with constant frequency $\gamma$, you can write the Lagrangian down. The potential energy can be written as $-mg(-...
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2answers
420 views

Why do planets move in fixed orbits?

Is it because the bending of space that occurs around the Sun creates a force acting on the planet which accelerates it towards the Sun (F=ma) while the planet has a tendency to move in a straight ...
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2answers
162 views

Why isn't the Time-Independent Schrödinger Equation an equation of motion?

I thought an equation of motion was something where you are given a Lagrangian and, using the Euler-Lagrange equation, you then find the equations of motion for that system. Same basic idea for the ...
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1answer
4k views

Does potential energy always equal kinetic energy?

When I studied physics in junior high and high school, we always took it for granted that potential energy was equal to kinetic energy. In Lagrangian terms, $T = V$at least on average. But I realized ...
3
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1answer
64 views

What is a sufficient condition to determine if the action integral reaches an extremal through the trajectory described by $q(t)$?

As I understand it, the Euler-Lagrange equation is a necessary but not a sufficient condition to determine if the action integral reaches an extremal through the trajectory described by $q(t)$. If ...
2
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1answer
123 views

What is an “equation of motion” as used in context of geodesic equation?

I am studying general relativity and using the book Gravity by James Hartle. On page 170, he provides the following table: I don't understand what he means by "equation of motion" nor do I ...
0
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1answer
608 views

Equations of motion for bob-on-a-string — am I missing some terms?

The dynamics of a type of physical system I am currently working on are modeled in most of the literature by replacing the moving parts of that system with an equivalent set of pendulums. Parameters ...
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3answers
8k views

What is “first order“ and “second order” in time?

What is the meaning of the text quoted below? In the physical world, if a system is described by an equation that is first order in time, the system is general dissipative (has energy loss). ...
2
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2answers
146 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C \...
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2answers
2k views

Given Angle, Initial Velocity, and Acceleration due to Gravity, plot parabolic trajectory for every “x”?

Given any Angle -> 0-90 Given any Initial Velocity -> 1-100 Given Acceleration due to Gravity -> 9.8 Plot every x,y coordinate (the parabolic trajectory) with cartesian coordinates and screen pixels (...
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0answers
117 views

Formulation of the Three-Body Newtonian problem

I am trying to understand three body problem in Newtonian space. I want to make formulation of differential equations for known initial conditions for the case with: Identical three masses ...
7
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3answers
878 views

Is there any case in physics where the equations of motion depend on high time derivatives of the position?

For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order ...
4
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1answer
158 views

Calculating equation of motion using path integral

Suppose my action integral is $S=\int d^4x(\nabla \times A)^2$ and $\delta S$ gives $\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$ I would like to calculate the coefficient of $\...
5
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0answers
649 views

General equation of motion for elementary particles

Elementary particles can be grouped into spin-classes and described by specific equations, see below: Is there a general Lagrangian density from which all these equations can be derived? A ...
1
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1answer
454 views

Control system with equation C = A*x + B*dx/dt

This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place ...
7
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2answers
2k views

Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the principle of least action for an explicitly time dependent Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
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3answers
1k views

What is the relationship between Schrödinger equation and Boltzmann equation?

The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics. ...
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1answer
631 views

Laws of Motion: Acceleration to be applied on a free falling object to reduce velocity to 0

Assume that an object of mass 'm' is falling to the earth.The force acting on the same would be F = m*g = 10m (assuming g = 10m/s^2). In this case the velocity of the object at time 't' = 10 seconds ...
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2answers
1k views

Question Concerning Position Of A Particle At Any Given Time

After years of procrastinating i've decided not to "move ahead" with physics without getting this ridiculously trivial question clear!*I know i had asked a similar question as silly and stupid as this ...
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3answers
255 views

Equation $H(q,p)=E$ is the equation of motion or energy-conservation law?

I do not completely understand, why do we consider Hamilton–Jacobi equation $H(q,p)=E$ as equation of motion, whereas it is looks like energy-conservation law?
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5answers
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Does the stress-energy tensor contain the equations of motion?

Derivatives $\nabla_i T^{ik}=0$ of a stress-energy tensor of physical system express conservation laws. Whether contains a stress-energy tensor also the information on the equations of motion of ...