The three-body problem is an application of Newton’s laws of motion where each of three bodies moves through space according to gravitational forces exerted by the other two bodies. Despite its simplicity, there is no general closed-form solution for the trajectories of the three bodies. However, you can approximate the trajectories with numerical methods. And since it’s … Continue reading Celestial OpenSeesing
Category: Rigid Body Dynamics
Double Inverted Pendulum
A double inverted pendulum (DIP) consists of two masses connected in series by rods to a pinned base. Without some form of control at the base, a DIP system is unstable. Consider the DIP shown below in the upright (inverted) position. The DIP is controlled by vertical base excitation, e.g., imparted by a motor with … Continue reading Double Inverted Pendulum
Spreader Beam Analysis
Problems involving beams are few and far between in Hibbeler 14th edition Engineering Mechanics: Dynamics. The problems mostly deal with springs, friction, pulleys, and things that rotate. So, Problem 15-3 was a welcome sight. A six foot long beam weighing 5000 lb is lifted from rest to a velocity of 8 ft/sec in 1.5 sec … Continue reading Spreader Beam Analysis
Faux Contact Sport
In a similar take on sprung masses and friction, it turns out that ENT+InitStrain in a zero length element is also an easy way to fake one-dimensional contact and impact. Consider Problem 14-23 from Hibbeler 14th edition. An 8 kg block, 2 m from a spring of stiffness 200 N/m, is given an initial velocity … Continue reading Faux Contact Sport
Two Sprung Masses and Some Friction Force
In Problem 13-13 from Hibbeler 14th edition, blocks A and B, of weight 8 lb and 6 lb, respectively, rest on a flat surface. A spring of stiffness 20 lb/ft is placed between the blocks. The blocks are pushed together, compressing the spring 0.2 ft, then the blocks are released to slide along the surface. … Continue reading Two Sprung Masses and Some Friction Force
Centripetal Acceleration
How can you induce element forces without defining loads or straining effects due to thermal expansion, residual stress, initial strain, or differential support motion? Centripetal acceleration! Get a mass revolving in a plane about a fixed point and a force directed radially (toward the center of revolution) is required to keep the mass from flying … Continue reading Centripetal Acceleration
Projectile OpenSeesing
Growing up in the Pine State, you were either a fan of NASCAR or college basketball, and in some cases both. I leaned heavily toward the latter. The hard dynamics underpins the physics of both sports--and most others. Centripetal forces act on race cars going around turns and projectile motion is a simplified description of … Continue reading Projectile OpenSeesing
No Element Required
Simulating basic particle motion raises subtle, often overlooked points about OpenSees. For example, consider problem 12-1 from Hibbeler's Engineering Mechanics: Dynamics, 14th edition. A particle moves along a straight line with acceleration a=(2t-6) m/s2. What is the velocity at t=6 s and displacement at t=11 s? Assume at rest initial conditions. By integration, the exact … Continue reading No Element Required
The Hard Dynamics
I am confident that you can use OpenSees to solve all reasonable problems from textbooks on statics, structural analysis, finite elements, structural dynamics, and (most of) strength of materials. But what about engineering dynamics? The rigid body dynamics that's way more difficult than deformable body dynamics. You know, kinematics and kinetics of particles and rigid … Continue reading The Hard Dynamics
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