# 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.

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### The product rule and the third kinematic equation

I'm trying to find physics-based examples for the rules of calculus. Using the product rule on the third kinematic equation to find the velocity is one such example. I'm deriving the correct equation ...
• 113
1 vote
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### Confusion about inverse kinematics of simple double-jointed arm

I hope this doesn't come across as too much of a check-my-work. If not, please let me know of a better site for this, or I'd appreciate being moved. I'll get straight to the point. I'm trying to ...
• 181
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### How to use BCH formula to compute mutiplication of group element?

i cant get the right answer. Given the commute rule of (for example, the caculation below will be in static group): we have: generator H, P, K, J, and commutation rule $[H,P]=0$, $[H,K]=0$, $[P,P]=0$...
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### Time to reach max height with an inverse square law relationship for gravity.

A spaceship is launched from Earth's surface with acceleration given by $$a = -\frac{gR^{2}}{x^{2}}$$ where $g$ is the acceleration due to gravity at the Earth's ...
42 views

### Covariant and contravariant velocity

I'm facing the following problem in tensor calculus: I want to calculate the velocity of a mass particle in spherical coordinates. So I'm using the following coordinate functions for spherical ...
20 views

### Rotating -axis relative motion, the acceleration of the origin of the rotating frame

I have a question of 3D kinematics of a rigid body. For relative motion analysis, let's define XYZ as an inertial frame, and xyz with origin O as a rotating frame. If we want to find the time ...
57 views

### Target position given ship velocity and bullet velocity.

Let's say we have two ships. Both have a velocity and the first ship has a turret with autotargeting. For simplicity let's say the ship is a point and a bullet comes out of that point. The first ship ...
• 15
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### Free-Surface kinematic BC - Azimuthal suspended flow - cylindrical coordinates - How to define the free surface and derive its impermeability?

I am working on a linear stability analysis of an azimuthal free surface flow. However, I am stuck in the derivation of the kinematic BC to apply for the impermeability of the azimuthal free surface (...
1 vote
31 views

### I have two formulations of quadrotor dynamics, one in euler angle velocities, and one in body frame angular velocities. I am unable to see equivalence

In the following MIT lecture notes Equation (6.10) is on the following form \begin{bmatrix} m \dot{v}^w \\ J \dot{\omega}^B \end{bmatrix} = \begin{bmatrix} -mge_3 \\ -\omega^B \times J ...
• 11
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### Why acceleration is not always parallel to velocity but velocity is always parallel to displacement?

Velocity is derivative of displacement : $$\vec v=\frac{\mathrm {d\vec r}}{\mathrm dt}$$ And acceleration is derivative of velocity. $$\vec a=\frac{\mathrm {d\vec v}}{\mathrm dt}$$ Given that their ...
• 2,821
1 vote
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### Circles,projectile motion and parabola

Q) A projectile is thrown at an angle theta from O(0,0) and reaches R(R,0) given R is the range of projectile A point P is taken on its trajectory and is joined with O(0,0) and R(R,0) such that angle ...
1 vote
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### Deriving the Maximum Range of a Particle With A Constant Force Using Geometric Algebra

I am learning Geometric Algebra by reading New Foundations for Classical Mechanics, by David Hestenes. Chapter 3-2 studies the motion of a particle with constant gravitational force and on page 129 ...
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### Maximizing Speed on an Elliptical Path

I'm currently delving into a problem that involves analyzing the motion of a particle moving along an elliptical path in the plane, and I could really use some help figuring out a couple of aspects. ...
1 vote
54 views

### Need Help with Particle Motion Analysis in $\mathbb{R}^2$

I'm currently working on a problem related to particle motion in the plane $( \mathbf{R}^2 )$ and could use some guidance. The particle moves along a curve, and at any given time $( t )$ seconds after ...
1 vote
94 views

### Time taken for a bead to slide down a wire.

A circular hoop of radius $r$ is stood vertically on a flat surface and held in place. A smooth wire is tightly stretched between the upmost point of the hoop and a point on the hoop at height $h$. A ...
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