packages that have some differential equations to solve and define some utility functions Needs "DifferentialEquations`NDSolveProblems`" ; Needs "DifferentialEquations`NDSolveUtilities`" ; Needs "DifferentialEquations`InterpolatingFunctionAnatomy` ; " Nee
Impact of a compound pendulum with a spring
Figure 1 depicts a uniform rod of mass m and length L and a spring with elastic constant k. The rod is connected to the ground by a pin joint and is free to rotate in a vertical plane and the end point of the ro
impact of a pendulum with a flat rigid surface packages that have some differential equations to solve and define some utility functions Needs "DifferentialEquations`NDSolveProblems`" ; Needs "DifferentialEquations`NDSolveUtilities`" ; Needs "Differential
Discontinuity in mechanics
In classical mechanics it was admitted the continuity of velocities, of accelerations and forces. The mechanical phenomena are continuous in time. There are cases when for very small time intervals there is a very large variatio
Impact of a sphere with a at surface
A sphere of mass m and radius R is impacting a at rigid surface with the initial velocity v0 . The sphere has the elastic modulus E1 and the rigid at surface has the elastic modulus E2 = E1 = E. The equivalent elastic
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H* packages that have some differential equations to solve and define some utility functions *L Needs@"DifferentialEquations`NDSolveProblems`"D; Needs@"DifferentialEquations`NDSolveUtilities`"D; Needs@"DifferentialEquations`InterpolatingFunction
v1 O1 O2
v2
O1
O2
v1 O1 u
v2 O2 u O1
u
u O2
v1
v2
v1
v2
O1
O2
Figure 2.1
u1
w1
1 O1 v1
O2 2
v2
u2
w2
(a)
u1
w1
1 O1
v1
O2 2
v2
u2
w2
(b)
Figure 2.2
w
v sin
e v cos
v
v cos
Figure 2.3
m1
1
H H1
2
v2 = 0 Figure P2.1
y
v2 O1 x O2 v1
Figure P2.2
x l
Dynamics: Newton-Euler Equations of Motion with Matlab
0
2
Direct Dynamics Newton-Euler Equations of Motion
mC = r F and ICzz = MC ,
The Newton-Euler equations of motion for a rigid body in plane motion are
or using the cartesian components mC = x Fx , mC
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CHAPTER
FLOW IN PIPES
luid flow in circular and noncircular pipes is commonly encountered in
practice. The hot and cold water that we use in our homes is pumped
through pipes. Water in a city is distributed by ext