The initial condition is defined as:determineIt is one of the conditions of various nuclear power plants with potential radiation emergency or emergency.It can be continuous and measurable performance parameters beyond the technical specifications, such as those that have been raisedReactor coolant systemTemperature or[1]Reactor coolantThe water level drops.
When we study a system, we take 0 as the starting time of the system, and the system state before the starting time is the 0 state.
The system state after the start time is the 0+state.
It is generally understood that 0 - means before power on, and 0+means after power on.
Principle of trim
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When t=0
(t) And derivatives of all orders should be balanced (other terms should also be balanced. We can discuss the initial conditions and ignore other terms)
Example:
r(t)+3r(t)=3
'(t), known (0 -), find r (0+)
The right end of the equation contains 3
(t) ,
3 must be included in
'(t), r (t) contains 3
(t)
The right end of the equation does not contain
(t) ,
It must contain - 9
(t) To balance 9 in 3r (t)
(t)
- 9 in
(t) In r (t), when t=0, there is - 9 △ u (t), and △ u (t) represents the relative jump function from 0 to 0+, so
r(0-)-r(0+)=-9
That is, r (0+)=r (0 -) - 9
Jump of starting point
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Response interval: after the excitation signal is added, the system state change interval is generally added at the time t=0, and the response interval is: 0+
For a specific electric network, the 0-state of the system is the energy storage condition of the energy storage elements in the system;
In general, the voltage at both ends of the capacitor and the current flowing through the inductance will not change abruptly during switching.This is the switching rule in circuit analysis:
However, when there is impulse current forcing on the capacitor or impulse voltage forcing on the inductor, the 0 - to 0+state will jump.
When the system is expressed by differential equation, whether the system jumps from 0 to 0+depends on whether the free term at the right end of the differential equation contains
(t) And derivative terms of each order.
physics
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1. The initial condition means that the initial state of the whole system is by no means the initial condition of an individual point u | t=0=φ (x)distribution function . ut | t=0=ψ (x), distribution function of initial velocity.
2. Initial conditions refer toHeat transfer processAt the beginning, the temperature of the whole object in the area is a known value, which can be expressed as 0 | t=0=0 0 or 0 | t=0=(x, y) by the formula, where 0 is a known constant, indicating that the initial temperature of the object is uniform.
3. Usually, the initial time (t=0 or t=t0) in the seepage areaheadThe distribution is called the initial condition.The initial time can be arbitrarily selected as required. For the two-dimensional problem H=H (x, y, t), the initial condition can be expressed as H (x, y, 0)=f (x, y) (x, y) ∈ D where (D) is the plane seepage region under study.
4. The initial condition is[2]boltThe disturbance state at the initial time t=0, usually refers to the initial displacement and initial velocity of the anchor rodacoustic emissionThe pulse excites the sensor to oscillate and generate the resistance oscillation waveform.
5. Humidity, wind direction, wind speed, etc. (all these are called initial conditions) to solve this equation set and calculate the distribution of atmospheric pressure, temperature, humidity, wind, etc. in the future.actuallyAtmospheric motionIt is quite complicated.
